diff --git a/modules/calib3d/src/calibration.cpp b/modules/calib3d/src/calibration.cpp
index 24d2875fdd..50940a80ff 100644
--- a/modules/calib3d/src/calibration.cpp
+++ b/modules/calib3d/src/calibration.cpp
@@ -3190,7 +3190,7 @@ cvRQDecomp3x3( const CvMat *matrixM, CvMat *matrixR, CvMat *matrixQ,
     */
     s = std::abs(matM[2][1]) > DBL_EPSILON ? matM[2][1] : 0;
     c = std::abs(matM[2][1]) > DBL_EPSILON ? matM[2][2] : 1;
-    z = 1./std::sqrt(c * c + s * s + DBL_EPSILON);
+    z = 1./std::sqrt(c * c + s * s);
     c *= z;
     s *= z;
 
@@ -3209,7 +3209,7 @@ cvRQDecomp3x3( const CvMat *matrixM, CvMat *matrixR, CvMat *matrixQ,
     */
     s = std::abs(matR[2][0]) > DBL_EPSILON ? -matR[2][0] : 0;
     c = std::abs(matR[2][0]) > DBL_EPSILON ? matR[2][2] : 1;
-    z = 1./std::sqrt(c * c + s * s + DBL_EPSILON);
+    z = 1./std::sqrt(c * c + s * s);
     c *= z;
     s *= z;
 
@@ -3229,7 +3229,7 @@ cvRQDecomp3x3( const CvMat *matrixM, CvMat *matrixR, CvMat *matrixQ,
 
     s = std::abs(matM[1][0]) > DBL_EPSILON ? matM[1][0] : 0;
     c = std::abs(matM[1][0]) > DBL_EPSILON ? matM[1][1] : 1;
-    z = 1./std::sqrt(c * c + s * s + DBL_EPSILON);
+    z = 1./std::sqrt(c * c + s * s);
     c *= z;
     s *= z;
 
diff --git a/modules/calib3d/test/test_decompose_projection.cpp b/modules/calib3d/test/test_decompose_projection.cpp
index 0e3a420d69..a25081b452 100644
--- a/modules/calib3d/test/test_decompose_projection.cpp
+++ b/modules/calib3d/test/test_decompose_projection.cpp
@@ -160,4 +160,24 @@ TEST(Calib3d_DecomposeProjectionMatrix, degenerate_cases)
     }
 }
 
+TEST(Calib3d_DecomposeProjectionMatrix, bug_23733)
+{
+    cv::Matx34d P(52, -7, 4, 12,
+                  -6, 49, 12, 8,
+                  4, 17, 1, 0);
+    P *= 1e-6;
+
+    cv::Matx33d K, R;
+    cv::Vec4d t;
+    decomposeProjectionMatrix(P, K, R, t);
+
+    EXPECT_LT(cv::norm(R.t() * R - cv::Matx33d::eye(), cv::NORM_INF), 1e-10);
+
+    cv::Matx34d M;
+    cv::hconcat(R, -R * cv::Vec3d(t[0] / t[3], t[1] / t[3], t[2] / t[3]), M);
+
+    cv::Matx34d P_recompose = K * M;
+    EXPECT_LT(cv::norm(P_recompose - P, cv::NORM_INF), 1e-16);
+}
+
 }} // namespace