diff --git a/modules/core/src/stat.cpp b/modules/core/src/stat.cpp
index 5b5b724f0..3d3b23e13 100644
--- a/modules/core/src/stat.cpp
+++ b/modules/core/src/stat.cpp
@@ -1270,7 +1270,7 @@ double cv::norm( InputArray _src, int normType, InputArray _mask )
     int depth = src.depth(), cn = src.channels();
     
     normType &= 7;
-    CV_Assert( normType == NORM_INF || normType == NORM_L1 || normType == NORM_L2 ||
+    CV_Assert( normType == NORM_INF || normType == NORM_L1 || normType == NORM_L2 || normType == NORM_L2SQR ||
                ((normType == NORM_HAMMING || normType == NORM_HAMMING2) && src.type() == CV_8U) );
     
     if( src.isContinuous() && mask.empty() )
@@ -1288,6 +1288,12 @@ double cv::norm( InputArray _src, int normType, InputArray _mask )
                     GET_OPTIMIZED(normL2_32f)(data, 0, &result, (int)len, 1);
                     return std::sqrt(result);
                 }
+                if( normType == NORM_L2SQR )
+                {
+                    double result = 0;
+                    GET_OPTIMIZED(normL2_32f)(data, 0, &result, (int)len, 1);
+                    return result;
+                }
                 if( normType == NORM_L1 )
                 {
                     double result = 0;
@@ -1354,7 +1360,7 @@ double cv::norm( InputArray _src, int normType, InputArray _mask )
     NAryMatIterator it(arrays, ptrs);
     int j, total = (int)it.size, blockSize = total, intSumBlockSize = 0, count = 0;
     bool blockSum = (normType == NORM_L1 && depth <= CV_16S) ||
-            (normType == NORM_L2 && depth <= CV_8S);
+            ((normType == NORM_L2 || normType == NORM_L2SQR) && depth <= CV_8S);
     int isum = 0;
     int *ibuf = &result.i;
     size_t esz = 0;
@@ -1413,7 +1419,7 @@ double cv::norm( InputArray _src1, InputArray _src2, int normType, InputArray _m
     CV_Assert( src1.size == src2.size && src1.type() == src2.type() );
     
     normType &= 7;
-    CV_Assert( normType == NORM_INF || normType == NORM_L1 || normType == NORM_L2 ||
+    CV_Assert( normType == NORM_INF || normType == NORM_L1 || normType == NORM_L2 || normType == NORM_L2SQR ||
               ((normType == NORM_HAMMING || normType == NORM_HAMMING2) && src1.type() == CV_8U) );
     
     if( src1.isContinuous() && src2.isContinuous() && mask.empty() )
@@ -1432,6 +1438,12 @@ double cv::norm( InputArray _src1, InputArray _src2, int normType, InputArray _m
                     GET_OPTIMIZED(normDiffL2_32f)(data1, data2, 0, &result, (int)len, 1);
                     return std::sqrt(result);
                 }
+                if( normType == NORM_L2SQR )
+                {
+                    double result = 0;
+                    GET_OPTIMIZED(normDiffL2_32f)(data1, data2, 0, &result, (int)len, 1);
+                    return result;
+                }
                 if( normType == NORM_L1 )
                 {
                     double result = 0;
@@ -1490,7 +1502,7 @@ double cv::norm( InputArray _src1, InputArray _src2, int normType, InputArray _m
     NAryMatIterator it(arrays, ptrs);
     int j, total = (int)it.size, blockSize = total, intSumBlockSize = 0, count = 0;
     bool blockSum = (normType == NORM_L1 && depth <= CV_16S) ||
-            (normType == NORM_L2 && depth <= CV_8S);
+            ((normType == NORM_L2 || normType == NORM_L2SQR) && depth <= CV_8S);
     unsigned isum = 0;
     unsigned *ibuf = &result.u;
     size_t esz = 0;
diff --git a/modules/core/test/test_arithm.cpp b/modules/core/test/test_arithm.cpp
index 3256cb7c1..7faa919e4 100644
--- a/modules/core/test/test_arithm.cpp
+++ b/modules/core/test/test_arithm.cpp
@@ -1227,11 +1227,17 @@ struct NormOp : public BaseElemWiseOp
     int getRandomType(RNG& rng)
     {
         int type = cvtest::randomType(rng, DEPTH_MASK_ALL_BUT_8S, 1, 4);
-        normType = 1 << rng.uniform(0, 3);
-        if( CV_MAT_DEPTH(type) == CV_8U && (rng.next() & 8) != 0 )
+        for(;;)
         {
-            normType = cv::NORM_HAMMING + rng.uniform(0, 2);
-            type = CV_MAT_DEPTH(type);
+            normType = rng.uniform(1, 8);
+            if( normType == NORM_INF || normType == NORM_L1 ||
+                normType == NORM_L2 || normType == NORM_L2SQR ||
+                normType == NORM_HAMMING || normType == NORM_HAMMING2 )
+                break;
+        }
+        if( normType == NORM_HAMMING || normType == NORM_HAMMING2 )
+        {
+            type = CV_8U;
         }
         return type;
     }
diff --git a/modules/ts/src/ts_func.cpp b/modules/ts/src/ts_func.cpp
index 103b29ea0..ee12665fe 100644
--- a/modules/ts/src/ts_func.cpp
+++ b/modules/ts/src/ts_func.cpp
@@ -1257,6 +1257,8 @@ double norm(const Mat& src, int normType, const Mat& mask)
             result += normHamming(planes[0].data, total, cellSize);
         return result;
     }
+    int normType0 = normType;
+    normType = normType == NORM_L2SQR ? NORM_L2 : normType;
     
     CV_Assert( mask.empty() || (src.size == mask.size && mask.type() == CV_8U) );
     CV_Assert( normType == NORM_INF || normType == NORM_L1 || normType == NORM_L2 );
@@ -1302,7 +1304,7 @@ double norm(const Mat& src, int normType, const Mat& mask)
             CV_Error(CV_StsUnsupportedFormat, "");
         };
     }
-    if( normType == NORM_L2 )
+    if( normType0 == NORM_L2 )
         result = sqrt(result);
     return result;
 }
@@ -1332,6 +1334,8 @@ double norm(const Mat& src1, const Mat& src2, int normType, const Mat& mask)
             result += normHamming(planes[0].data, total, cellSize);
         return result;
     }
+    int normType0 = normType;
+    normType = normType == NORM_L2SQR ? NORM_L2 : normType;
     
     CV_Assert( src1.type() == src2.type() && src1.size == src2.size );
     CV_Assert( mask.empty() || (src1.size == mask.size && mask.type() == CV_8U) );
@@ -1378,7 +1382,7 @@ double norm(const Mat& src1, const Mat& src2, int normType, const Mat& mask)
             CV_Error(CV_StsUnsupportedFormat, "");
         };
     }
-    if( normType == NORM_L2 )
+    if( normType0 == NORM_L2 )
         result = sqrt(result);
     return result;
 }