diff --git a/modules/calib3d/src/calibration.cpp b/modules/calib3d/src/calibration.cpp
index 9bc48661e3..d24bc90d1b 100644
--- a/modules/calib3d/src/calibration.cpp
+++ b/modules/calib3d/src/calibration.cpp
@@ -2297,7 +2297,7 @@ void cvStereoRectify( const CvMat* _cameraMatrix1, const CvMat* _cameraMatrix2,
                       CvRect* roi1, CvRect* roi2 )
 {
     double _om[3], _t[3] = {0}, _uu[3]={0,0,0}, _r_r[3][3], _pp[3][4];
-    double _ww[3], _wr[3][3], _z[3] = {0,0,0}, _ri[3][3], _w3[3];
+    double _ww[3], _wr[3][3], _z[3] = {0,0,0}, _ri[3][3];
     cv::Rect_<float> inner1, inner2, outer1, outer2;
 
     CvMat om  = cvMat(3, 1, CV_64F, _om);
@@ -2306,13 +2306,11 @@ void cvStereoRectify( const CvMat* _cameraMatrix1, const CvMat* _cameraMatrix2,
     CvMat r_r = cvMat(3, 3, CV_64F, _r_r);
     CvMat pp  = cvMat(3, 4, CV_64F, _pp);
     CvMat ww  = cvMat(3, 1, CV_64F, _ww); // temps
-    CvMat w3  = cvMat(3, 1, CV_64F, _w3); // temps
     CvMat wR  = cvMat(3, 3, CV_64F, _wr);
     CvMat Z   = cvMat(3, 1, CV_64F, _z);
     CvMat Ri  = cvMat(3, 3, CV_64F, _ri);
     double nx = imageSize.width, ny = imageSize.height;
     int i, k;
-    double nt, nw;
 
     if( matR->rows == 3 && matR->cols == 3 )
         cvRodrigues2(matR, &om);          // get vector rotation
@@ -2323,36 +2321,15 @@ void cvStereoRectify( const CvMat* _cameraMatrix1, const CvMat* _cameraMatrix2,
     cvMatMul(&r_r, matT, &t);
 
     int idx = fabs(_t[0]) > fabs(_t[1]) ? 0 : 1;
+    double c = _t[idx], nt = cvNorm(&t, 0, CV_L2);
+    _uu[idx] = c > 0 ? 1 : -1;
 
-    // if idx == 0
-    //   e1 = T / ||T||
-    //   e2 = e1 x [0,0,1]
-
-    // if idx == 1
-    //   e2 = T / ||T||
-    //   e1 = e2 x [0,0,1]
-
-    // e3 = e1 x e2
-
-    _uu[2] = 1;
-    cvCrossProduct(&uu, &t, &ww);
-    nt = cvNorm(&t, 0, CV_L2);
-    CV_Assert(fabs(nt) > 0);
-    nw = cvNorm(&ww, 0, CV_L2);
-    CV_Assert(fabs(nw) > 0);
-    cvConvertScale(&ww, &ww, 1 / nw);
-    cvCrossProduct(&t, &ww, &w3);
-    nw = cvNorm(&w3, 0, CV_L2);
-    CV_Assert(fabs(nw) > 0);
-    cvConvertScale(&w3, &w3, 1 / nw);
-    _uu[2] = 0;
-
-    for (i = 0; i < 3; ++i)
-    {
-        _wr[idx][i] = -_t[i] / nt;
-        _wr[idx ^ 1][i] = -_ww[i];
-        _wr[2][i] = _w3[i] * (1 - 2 * idx); // if idx == 1 -> opposite direction
-    }
+    // calculate global Z rotation
+    cvCrossProduct(&t,&uu,&ww);
+    double nw = cvNorm(&ww, 0, CV_L2);
+    if (nw > 0.0)
+        cvConvertScale(&ww, &ww, acos(fabs(c)/nt)/nw);
+    cvRodrigues2(&ww, &wR);
 
     // apply to both views
     cvGEMM(&wR, &r_r, 1, 0, 0, &Ri, CV_GEMM_B_T);
diff --git a/modules/calib3d/test/test_cameracalibration.cpp b/modules/calib3d/test/test_cameracalibration.cpp
index adf4e454be..7aeaea3021 100644
--- a/modules/calib3d/test/test_cameracalibration.cpp
+++ b/modules/calib3d/test/test_cameracalibration.cpp
@@ -2332,6 +2332,44 @@ TEST(Calib3d_StereoCalibrate, regression_10791)
     EXPECT_GE(roi2.area(), 400*300) << roi2;
 }
 
+TEST(Calib3d_StereoCalibrate, regression_11131)
+{
+    const Matx33d M1(
+        1457.572438721727, 0, 1212.945694211622,
+        0, 1457.522226502963, 1007.32058848921,
+        0, 0, 1
+    );
+    const Matx33d M2(
+        1460.868570835972, 0, 1215.024068023046,
+        0, 1460.791367088, 1011.107202932225,
+        0, 0, 1
+    );
+    const Matx<double, 5, 1> D1(0, 0, 0, 0, 0);
+    const Matx<double, 5, 1> D2(0, 0, 0, 0, 0);
+
+    const Matx33d R(
+        0.9985404059825475, 0.02963547172078553, -0.04515303352041626,
+        -0.03103795276460111, 0.9990471552537432, -0.03068268351343364,
+        0.04420071389006859, 0.03203935697372317, 0.9985087763742083
+    );
+    const Matx31d T(0.9995500167379527, 0.0116311595111068, 0.02764923448462666);
+
+    const Size imageSize(2456, 2058);
+
+    Mat R1, R2, P1, P2, Q;
+    Rect roi1, roi2;
+    stereoRectify(M1, D1, M2, D2, imageSize, R, T,
+                  R1, R2, P1, P2, Q,
+                  CALIB_ZERO_DISPARITY, 1, imageSize, &roi1, &roi2);
+
+    EXPECT_GT(P1.at<double>(0, 0), 0);
+    EXPECT_GT(P2.at<double>(0, 0), 0);
+    EXPECT_GT(R1.at<double>(0, 0), 0);
+    EXPECT_GT(R2.at<double>(0, 0), 0);
+    EXPECT_GE(roi1.area(), 400*300) << roi1;
+    EXPECT_GE(roi2.area(), 400*300) << roi2;
+}
+
 TEST(Calib3d_Triangulate, accuracy)
 {
     // the testcase from http://code.opencv.org/issues/4334