diff --git a/addons/mail/static/src/components/chat_window_header/chat_window_header.js b/addons/mail/static/src/components/chat_window_header/chat_window_header.js
index 697a952508a..eb78f4c4390 100644
--- a/addons/mail/static/src/components/chat_window_header/chat_window_header.js
+++ b/addons/mail/static/src/components/chat_window_header/chat_window_header.js
@@ -41,6 +41,26 @@ class ChatWindowHeader extends Component {
         return this.env.models['mail.chat_window'].get(this.props.chatWindowLocalId);
     }
 
+    /**
+     * @returns {string}
+     */
+    get shiftNextText() {
+        if (this.env.messaging.locale.textDirection === 'rtl') {
+            return this.env._t("Shift left");
+        }
+        return this.env._t("Shift right");
+    }
+
+    /**
+     * @returns {string}
+     */
+    get shiftPrevText() {
+        if (this.env.messaging.locale.textDirection === 'rtl') {
+            return this.env._t("Shift right");
+        }
+        return this.env._t("Shift left");
+    }
+
     //--------------------------------------------------------------------------
     // Handlers
     //--------------------------------------------------------------------------
@@ -53,6 +73,12 @@ class ChatWindowHeader extends Component {
         if (isEventHandled(ev, 'ChatWindowHeader.openProfile')) {
             return;
         }
+        if (isEventHandled(ev, 'ChatWindowHeader.ClickShiftNext')) {
+            return;
+        }
+        if (isEventHandled(ev, 'ChatWindowHeader.ClickShiftPrev')) {
+            return;
+        }
         const chatWindow = this.chatWindow;
         this.trigger('o-clicked', { chatWindow });
     }
@@ -90,18 +116,18 @@ class ChatWindowHeader extends Component {
      * @private
      * @param {MouseEvent} ev
      */
-    _onClickShiftLeft(ev) {
-        ev.stopPropagation();
-        this.chatWindow.shiftLeft();
+    _onClickShiftPrev(ev) {
+        markEventHandled(ev, 'ChatWindowHeader.ClickShiftPrev');
+        this.chatWindow.shiftPrev();
     }
 
     /**
      * @private
      * @param {MouseEvent} ev
      */
-    _onClickShiftRight(ev) {
-        ev.stopPropagation();
-        this.chatWindow.shiftRight();
+    _onClickShiftNext(ev) {
+        markEventHandled(ev, 'ChatWindowHeader.ClickShiftNext');
+        this.chatWindow.shiftNext();
     }
 
 }
diff --git a/addons/mail/static/src/components/chat_window_header/chat_window_header.xml b/addons/mail/static/src/components/chat_window_header/chat_window_header.xml
index 47c59470895..fc8a324992f 100644
--- a/addons/mail/static/src/components/chat_window_header/chat_window_header.xml
+++ b/addons/mail/static/src/components/chat_window_header/chat_window_header.xml
@@ -28,13 +28,15 @@
                 </t>
                 <div class="o-autogrow"/>
                 <div class="o_ChatWindowHeader_item o_ChatWindowHeader_rightArea">
-                    <t t-if="chatWindow.hasShiftLeft">
-                        <div class="o_ChatWindowHeader_command o_ChatWindowHeader_commandShiftLeft" t-att-class="{ 'o-mobile': env.messaging.device.isMobile }" t-on-click="_onClickShiftLeft" title="Shift left">
+                    <t t-if="chatWindow.hasShiftPrev">
+                        <div class="o_ChatWindowHeader_command o_ChatWindowHeader_commandShiftPrev" t-att-class="{ 'o-mobile': env.messaging.device.isMobile }" t-on-click="_onClickShiftPrev" t-att-title="shiftPrevText">
+                            <!-- this is reversed automatically when language is rtl -->
                             <i class="fa fa-angle-left"/>
                         </div>
                     </t>
-                    <t t-if="chatWindow.hasShiftRight">
-                        <div class="o_ChatWindowHeader_command o_ChatWindowHeader_commandShiftRight" t-att-class="{ 'o-mobile': env.messaging.device.isMobile }" t-on-click="_onClickShiftRight" title="Shift right">
+                    <t t-if="chatWindow.hasShiftNext">
+                        <div class="o_ChatWindowHeader_command o_ChatWindowHeader_commandShiftNext" t-att-class="{ 'o-mobile': env.messaging.device.isMobile }" t-on-click="_onClickShiftNext" t-att-title="shiftNextText">
+                            <!-- this is reversed automatically when language is rtl -->
                             <i class="fa fa-angle-right"/>
                         </div>
                     </t>
diff --git a/addons/mail/static/src/components/chat_window_manager/chat_window_manager_tests.js b/addons/mail/static/src/components/chat_window_manager/chat_window_manager_tests.js
index e76ff23fc38..626411577fd 100644
--- a/addons/mail/static/src/components/chat_window_manager/chat_window_manager_tests.js
+++ b/addons/mail/static/src/components/chat_window_manager/chat_window_manager_tests.js
@@ -11,6 +11,7 @@ const {
 } = require('mail/static/src/utils/test_utils.js');
 
 const Bus = require('web.Bus');
+const core = require('web.core');
 const {
     file: { createFile, inputFiles },
     dom: { triggerEvent },
@@ -337,7 +338,7 @@ QUnit.test('open chat from "new message" chat window should open chat in place o
     );
 
     await afterNextRender(() =>
-        document.querySelector('.o_ChatWindow[data-visible-index="2"] .o_ChatWindowHeader_commandShiftRight').click()
+        document.querySelector('.o_ChatWindow[data-visible-index="2"] .o_ChatWindowHeader_commandShiftNext').click()
     );
     assert.hasClass(
         document.querySelector('.o_ChatWindow[data-visible-index="1"]'),
@@ -1064,22 +1065,22 @@ QUnit.test('open 2 chat windows: check shift operations are available', async fu
     );
     assert.containsOnce(
         document.querySelectorAll('.o_ChatWindow')[0],
-        '.o_ChatWindowHeader_commandShiftLeft',
+        '.o_ChatWindowHeader_commandShiftPrev',
         "first chat window should be allowed to shift left"
     );
     assert.containsNone(
         document.querySelectorAll('.o_ChatWindow')[0],
-        '.o_ChatWindowHeader_commandShiftRight',
+        '.o_ChatWindowHeader_commandShiftNext',
         "first chat window should not be allowed to shift right"
     );
     assert.containsNone(
         document.querySelectorAll('.o_ChatWindow')[1],
-        '.o_ChatWindowHeader_commandShiftLeft',
+        '.o_ChatWindowHeader_commandShiftPrev',
         "second chat window should not be allowed to shift left"
     );
     assert.containsOnce(
         document.querySelectorAll('.o_ChatWindow')[1],
-        '.o_ChatWindowHeader_commandShiftRight',
+        '.o_ChatWindowHeader_commandShiftNext',
         "second chat window should be allowed to shift right"
     );
 
@@ -1089,7 +1090,7 @@ QUnit.test('open 2 chat windows: check shift operations are available', async fu
         document.querySelectorAll('.o_ChatWindow')[1].dataset.threadLocalId;
     await afterNextRender(() => {
         document.querySelectorAll('.o_ChatWindow')[0]
-            .querySelector(':scope .o_ChatWindowHeader_commandShiftLeft')
+            .querySelector(':scope .o_ChatWindowHeader_commandShiftPrev')
             .click();
     });
     assert.strictEqual(
@@ -1105,7 +1106,7 @@ QUnit.test('open 2 chat windows: check shift operations are available', async fu
 
     await afterNextRender(() => {
         document.querySelectorAll('.o_ChatWindow')[1]
-            .querySelector(':scope .o_ChatWindowHeader_commandShiftRight')
+            .querySelector(':scope .o_ChatWindowHeader_commandShiftNext')
             .click();
     });
     assert.strictEqual(
@@ -1176,12 +1177,12 @@ QUnit.test('open 2 folded chat windows: check shift operations are available', a
     );
     assert.containsOnce(
         document.body,
-        '.o_ChatWindow .o_ChatWindowHeader_commandShiftLeft',
+        '.o_ChatWindow .o_ChatWindowHeader_commandShiftPrev',
         "there should be only one chat window allowed to shift left even if folded"
     );
     assert.containsOnce(
         document.body,
-        '.o_ChatWindow .o_ChatWindowHeader_commandShiftRight',
+        '.o_ChatWindow .o_ChatWindowHeader_commandShiftNext',
         "there should be only one chat window allowed to shift right even if folded"
     );
 
@@ -1190,7 +1191,7 @@ QUnit.test('open 2 folded chat windows: check shift operations are available', a
     const initialSecondChatWindowThreadLocalId =
         document.querySelector('.o_ChatWindow[data-visible-index="1"]').dataset.threadLocalId;
     await afterNextRender(() =>
-        document.querySelector('.o_ChatWindowHeader_commandShiftLeft').click()
+        document.querySelector('.o_ChatWindowHeader_commandShiftPrev').click()
     );
     assert.strictEqual(
         document.querySelector('.o_ChatWindow[data-visible-index="0"]').dataset.threadLocalId,
@@ -1204,7 +1205,7 @@ QUnit.test('open 2 folded chat windows: check shift operations are available', a
     );
 
     await afterNextRender(() =>
-        document.querySelector('.o_ChatWindowHeader_commandShiftLeft').click()
+        document.querySelector('.o_ChatWindowHeader_commandShiftPrev').click()
     );
     assert.strictEqual(
         document.querySelector('.o_ChatWindow[data-visible-index="0"]').dataset.threadLocalId,
@@ -1218,7 +1219,7 @@ QUnit.test('open 2 folded chat windows: check shift operations are available', a
     );
 
     await afterNextRender(() =>
-        document.querySelector('.o_ChatWindowHeader_commandShiftRight').click()
+        document.querySelector('.o_ChatWindowHeader_commandShiftNext').click()
     );
     assert.strictEqual(
         document.querySelector('.o_ChatWindow[data-visible-index="0"]').dataset.threadLocalId,
@@ -1232,7 +1233,7 @@ QUnit.test('open 2 folded chat windows: check shift operations are available', a
     );
 
     await afterNextRender(() =>
-        document.querySelector('.o_ChatWindowHeader_commandShiftRight').click()
+        document.querySelector('.o_ChatWindowHeader_commandShiftNext').click()
     );
     assert.strictEqual(
         document.querySelector('.o_ChatWindow[data-visible-index="0"]').dataset.threadLocalId,
@@ -2181,6 +2182,64 @@ QUnit.test('chat window: chat header should not be clickable when thread has mul
     );
 });
 
+QUnit.test('Textual representations of shift previous/next operations are correctly mapped to left/right in LTR locale', async function (assert) {
+    assert.expect(2);
+
+    this.data['mail.channel'].records.push(
+        { is_minimized: true },
+        { is_minimized: true },
+    );
+    await this.start();
+
+    assert.strictEqual(
+        document.querySelector('.o_ChatWindowHeader_commandShiftPrev').title,
+        "Shift left",
+        "shift previous operation should be have 'Shift left' as title in LTR locale"
+    );
+    assert.strictEqual(
+        document.querySelector('.o_ChatWindowHeader_commandShiftNext').title,
+        "Shift right",
+        "shift next operation should have 'Shift right' as title in LTR locale"
+    );
+});
+
+QUnit.test('Textual representations of shift previous/next operations are correctly mapped to right/left in RTL locale', async function (assert) {
+    assert.expect(2);
+
+    this.data['mail.channel'].records.push(
+        { is_minimized: true },
+        { is_minimized: true },
+    );
+    await this.start({
+        env: {
+            _t: Object.assign((s => s), {
+                database: {
+                    parameters: {
+                        code: "en_US",
+                        date_format: '%m/%d/%Y',
+                        decimal_point: ".",
+                        direction: 'rtl',
+                        grouping: [],
+                        thousands_sep: ",",
+                        time_format: '%H:%M:%S',
+                    },
+                },
+            }),
+        }
+    });
+
+    assert.strictEqual(
+        document.querySelector('.o_ChatWindowHeader_commandShiftPrev').title,
+        "Shift right",
+        "shift previous operation should have 'Shift right' as title in RTL locale"
+    );
+    assert.strictEqual(
+        document.querySelector('.o_ChatWindowHeader_commandShiftNext').title,
+        "Shift left",
+        "shift next operation should have 'Shift left' as title in RTL locale"
+    );
+});
+
 });
 });
 });
diff --git a/addons/mail/static/src/models/chat_window/chat_window.js b/addons/mail/static/src/models/chat_window/chat_window.js
index 4a38ef91f34..4d51d952696 100644
--- a/addons/mail/static/src/models/chat_window/chat_window.js
+++ b/addons/mail/static/src/models/chat_window/chat_window.js
@@ -118,17 +118,17 @@ function factory(dependencies) {
         }
 
         /**
-         * Shift this chat window to the left on screen.
+         * Swap this chat window with the previous one.
          */
-        shiftLeft() {
-            this.manager.shiftLeft(this);
+        shiftPrev() {
+            this.manager.shiftPrev(this);
         }
 
         /**
-         * Shift this chat window to the right on screen.
+         * Swap this chat window with the next one.
          */
-        shiftRight() {
-            this.manager.shiftRight(this);
+        shiftNext() {
+            this.manager.shiftNext(this);
         }
 
         /**
@@ -160,7 +160,7 @@ function factory(dependencies) {
          * @private
          * @returns {boolean}
          */
-        _computeHasShiftLeft() {
+        _computeHasShiftPrev() {
             if (!this.manager) {
                 return false;
             }
@@ -176,7 +176,7 @@ function factory(dependencies) {
          * @private
          * @returns {boolean}
          */
-        _computeHasShiftRight() {
+        _computeHasShiftNext() {
             if (!this.manager) {
                 return false;
             }
@@ -342,13 +342,13 @@ function factory(dependencies) {
                 'thread',
             ],
         }),
-        hasShiftLeft: attr({
-            compute: '_computeHasShiftLeft',
+        hasShiftPrev: attr({
+            compute: '_computeHasShiftPrev',
             dependencies: ['managerAllOrderedVisible'],
             default: false,
         }),
-        hasShiftRight: attr({
-            compute: '_computeHasShiftRight',
+        hasShiftNext: attr({
+            compute: '_computeHasShiftNext',
             dependencies: ['managerAllOrderedVisible'],
             default: false,
         }),
diff --git a/addons/mail/static/src/models/chat_window_manager/chat_window_manager.js b/addons/mail/static/src/models/chat_window_manager/chat_window_manager.js
index 88fb24c1b1c..958ce8f9652 100644
--- a/addons/mail/static/src/models/chat_window_manager/chat_window_manager.js
+++ b/addons/mail/static/src/models/chat_window_manager/chat_window_manager.js
@@ -141,15 +141,16 @@ function factory(dependencies) {
         }
 
         /**
-         * Shift provided chat window to the left on screen.
+         * Shift provided chat window to previous visible index, which swap visible order of this
+         * chat window and the preceding visible one
          *
          * @param {mail.chat_window} chatWindow
          */
-        shiftLeft(chatWindow) {
+        shiftPrev(chatWindow) {
             const chatWindows = this.allOrdered;
             const index = chatWindows.findIndex(cw => cw === chatWindow);
             if (index === chatWindows.length - 1) {
-                // already left-most
+                // already first one
                 return;
             }
             const otherChatWindow = chatWindows[index + 1];
@@ -161,15 +162,16 @@ function factory(dependencies) {
         }
 
         /**
-         * Shift provided chat window to the right on screen.
+         * Shift provided chat window to next visible index, which swap visible order of this
+         * chat window and the following visible one.
          *
          * @param {mail.chat_window} chatWindow
          */
-        shiftRight(chatWindow) {
+        shiftNext(chatWindow) {
             const chatWindows = this.allOrdered;
             const index = chatWindows.findIndex(cw => cw === chatWindow);
             if (index === 0) {
-                // already right-most
+                // already last one
                 return;
             }
             const otherChatWindow = chatWindows[index - 1];