diff --git a/src/widgets/widgets/qdockwidget.cpp b/src/widgets/widgets/qdockwidget.cpp
index a3c331aa2b..ae931deb16 100644
--- a/src/widgets/widgets/qdockwidget.cpp
+++ b/src/widgets/widgets/qdockwidget.cpp
@@ -1259,6 +1259,9 @@ void QDockWidget::setFloating(bool floating)
         d->endDrag(true);
 
     QRect r = d->undockedGeometry;
+    // Keep position when undocking for the first time.
+    if (floating && isVisible() && !r.isValid())
+        r = QRect(mapToGlobal(QPoint(0, 0)), size());
 
     d->setWindowState(floating, false, floating ? r : QRect());
 
diff --git a/tests/auto/widgets/widgets/qdockwidget/tst_qdockwidget.cpp b/tests/auto/widgets/widgets/qdockwidget/tst_qdockwidget.cpp
index 6ab7cb4491..a4ad18c7a6 100644
--- a/tests/auto/widgets/widgets/qdockwidget/tst_qdockwidget.cpp
+++ b/tests/auto/widgets/widgets/qdockwidget/tst_qdockwidget.cpp
@@ -347,7 +347,9 @@ void tst_QDockWidget::features()
 
 void tst_QDockWidget::setFloating()
 {
+    const QRect deskRect = QApplication::desktop()->availableGeometry();
     QMainWindow mw;
+    mw.move(deskRect.left() + deskRect.width() * 2 / 3, deskRect.top() + deskRect.height() / 3);
     QDockWidget dw;
     mw.addDockWidget(Qt::LeftDockWidgetArea, &dw);
 
@@ -355,10 +357,16 @@ void tst_QDockWidget::setFloating()
     QVERIFY(QTest::qWaitForWindowExposed(&mw));
 
     QVERIFY(!dw.isFloating());
+    const QPoint dockedPosition = dw.mapToGlobal(dw.pos());
 
     QSignalSpy spy(&dw, SIGNAL(topLevelChanged(bool)));
 
     dw.setFloating(true);
+    const QPoint floatingPosition = dw.pos();
+
+    // QTBUG-31044, show approximately at old position, give or take window frame.
+    QVERIFY((dockedPosition - floatingPosition).manhattanLength() < 50);
+
     QVERIFY(dw.isFloating());
     QCOMPARE(spy.count(), 1);
     QCOMPARE(spy.at(0).value(0).toBool(), dw.isFloating());