diff --git a/modules/calib3d/src/calibration.cpp b/modules/calib3d/src/calibration.cpp
index 70f2aafede..98deab6396 100644
--- a/modules/calib3d/src/calibration.cpp
+++ b/modules/calib3d/src/calibration.cpp
@@ -820,9 +820,9 @@ CV_IMPL void cvProjectPoints2( const CvMat* objectPoints,
                         {
                             dpdk_p[5] = fx*x*cdist*(-icdist2)*icdist2*r2;
                             dpdk_p[dpdk_step+5] = fy*y*cdist*(-icdist2)*icdist2*r2;
-                            dpdk_p[6] = fx*x*icdist2*cdist*(-icdist2)*icdist2*r4;
+                            dpdk_p[6] = fx*x*cdist*(-icdist2)*icdist2*r4;
                             dpdk_p[dpdk_step+6] = fy*y*cdist*(-icdist2)*icdist2*r4;
-                            dpdk_p[7] = fx*x*icdist2*cdist*(-icdist2)*icdist2*r6;
+                            dpdk_p[7] = fx*x*cdist*(-icdist2)*icdist2*r6;
                             dpdk_p[dpdk_step+7] = fy*y*cdist*(-icdist2)*icdist2*r6;
                             if( _dpdk->cols > 8 )
                             {
diff --git a/modules/calib3d/test/test_cameracalibration.cpp b/modules/calib3d/test/test_cameracalibration.cpp
index 9d7145ee14..2053e0677b 100644
--- a/modules/calib3d/test/test_cameracalibration.cpp
+++ b/modules/calib3d/test/test_cameracalibration.cpp
@@ -1876,9 +1876,11 @@ TEST(Calib3d_ProjectPoints_CPP, regression) { CV_ProjectPointsTest_CPP test; tes
 TEST(Calib3d_StereoCalibrate_C, regression) { CV_StereoCalibrationTest_C test; test.safe_run(); }
 TEST(Calib3d_StereoCalibrate_CPP, regression) { CV_StereoCalibrationTest_CPP test; test.safe_run(); }
 
-// the testcase by Christian Richardt
+
 TEST(Calib3d_Triangulate, accuracy)
 {
+    // the testcase from http://code.opencv.org/issues/4334
+    {
     double P1data[] = { 250, 0, 200, 0, 0, 250, 150, 0, 0, 0, 1, 0 };
     double P2data[] = { 250, 0, 200, -250, 0, 250, 150, 0, 0, 0, 1, 0 };
     Mat P1(3, 4, CV_64F, P1data), P2(3, 4, CV_64F, P2data);
@@ -1896,8 +1898,50 @@ TEST(Calib3d_Triangulate, accuracy)
     convertPointsFromHomogeneous(res_, res);
     res = res.reshape(1, 1);
 
-    cout << "res0: " << res0 << endl;
-    cout << "res: " << res << endl;
+    cout << "[1]:" << endl;
+    cout << "\tres0: " << res0 << endl;
+    cout << "\tres: " << res << endl;
 
     ASSERT_LE(norm(res, res0, NORM_INF), 1e-1);
+    }
+
+    // another testcase http://code.opencv.org/issues/3461
+    {
+    Matx33d K1(6137.147949, 0.000000, 644.974609,
+               0.000000, 6137.147949, 573.442749,
+               0.000000, 0.000000,  1.000000);
+    Matx33d K2(6137.147949,  0.000000, 644.674438,
+               0.000000, 6137.147949, 573.079834,
+               0.000000,  0.000000, 1.000000);
+
+    Matx34d RT1(1, 0, 0, 0,
+                0, 1, 0, 0,
+                0, 0, 1, 0);
+
+    Matx34d RT2(0.998297, 0.0064108, -0.0579766,     143.614334,
+               -0.0065818, 0.999975, -0.00275888,   -5.160085,
+               0.0579574, 0.00313577, 0.998314,     96.066109);
+
+    Matx34d P1 = K1*RT1;
+    Matx34d P2 = K2*RT2;
+
+    float x1data[] = { 438.f, 19.f };
+    float x2data[] = { 452.363600f, 16.452225f };
+    float Xdata[] = { -81.049530f, -215.702804f, 2401.645449f };
+    Mat x1(2, 1, CV_32F, x1data);
+    Mat x2(2, 1, CV_32F, x2data);
+    Mat res0(1, 3, CV_32F, Xdata);
+    Mat res_, res;
+
+    triangulatePoints(P1, P2, x1, x2, res_);
+    transpose(res_, res_);
+    convertPointsFromHomogeneous(res_, res);
+    res = res.reshape(1, 1);
+
+    cout << "[2]:" << endl;
+    cout << "\tres0: " << res0 << endl;
+    cout << "\tres: " << res << endl;
+
+    ASSERT_LE(norm(res, res0, NORM_INF), 2);
+    }
 }