diff --git a/modules/calib3d/src/fisheye.cpp b/modules/calib3d/src/fisheye.cpp
index 3ed9ba43f1..96d74cc141 100644
--- a/modules/calib3d/src/fisheye.cpp
+++ b/modules/calib3d/src/fisheye.cpp
@@ -388,10 +388,18 @@ void cv::fisheye::undistortPoints( InputArray distorted, OutputArray undistorted
         {
             // compensate distortion iteratively
             double theta = theta_d;
-            for(int j = 0; j < 10; j++ )
+
+            const double EPS = 1e-8; // or std::numeric_limits<double>::epsilon();
+            for (int j = 0; j < 10; j++)
             {
                 double theta2 = theta*theta, theta4 = theta2*theta2, theta6 = theta4*theta2, theta8 = theta6*theta2;
-                theta = theta_d / (1 + k[0] * theta2 + k[1] * theta4 + k[2] * theta6 + k[3] * theta8);
+                double k0_theta2 = k[0] * theta2, k1_theta4 = k[1] * theta4, k2_theta6 = k[2] * theta6, k3_theta8 = k[3] * theta8;
+                /* new_theta = theta - theta_fix, theta_fix = f0(theta) / f0'(theta) */
+                double theta_fix = (theta * (1 + k0_theta2 + k1_theta4 + k2_theta6 + k3_theta8) - theta_d) /
+                                   (1 + 3*k0_theta2 + 5*k1_theta4 + 7*k2_theta6 + 9*k3_theta8);
+                theta = theta - theta_fix;
+                if (fabs(theta_fix) < EPS)
+                    break;
             }
 
             scale = std::tan(theta) / theta_d;