diff --git a/src/lib/validate-input.js b/src/lib/validate-input.js
index f437aa4..f9e95bf 100644
--- a/src/lib/validate-input.js
+++ b/src/lib/validate-input.js
@@ -454,7 +454,7 @@ export function validateTriangularParams(input, {diagonal = 0} = {}) {
   if (i !== j) {
     throw new Error('The input should be a 2-D tensor of [N, N] shape.');
   }
-  if (!Number.isInteger(diagonal) || diagonal >= i || diagonal <= -i) {
-    throw new Error(`The diagonal should be an integer in the interval [${1 - i}, ${i - 1}].`);
+  if (!Number.isInteger(diagonal)) {
+    throw new Error(`The diagonal should be an integer.`);
   }
 }
diff --git a/test/triangular_test.js b/test/triangular_test.js
index 4c29eb6..5763104 100644
--- a/test/triangular_test.js
+++ b/test/triangular_test.js
@@ -57,6 +57,30 @@ describe('test triangular', function() {
     );
   });
 
+  it('triangular fully zero diagonal=4', function() {
+    testTriangular(
+        {
+          shape: [3, 3],
+          data: [
+            7, 1, 2,
+            9, 4, 8,
+            2, 6, 3,
+          ],
+        },
+        {
+          shape: [3, 3],
+          data: [
+            0, 0, 0,
+            0, 0, 0,
+            0, 0, 0,
+          ],
+        },
+        {
+          diagonal: 4,
+        },
+    );
+  });
+
   it('triangular diagonal=-1', function() {
     testTriangular(
         {
@@ -81,6 +105,30 @@ describe('test triangular', function() {
     );
   });
 
+  it('triangular fully copied diagonal=-4', function() {
+    testTriangular(
+        {
+          shape: [3, 3],
+          data: [
+            7, 1, 2,
+            9, 4, 8,
+            2, 6, 3,
+          ],
+        },
+        {
+          shape: [3, 3],
+          data: [
+            7, 1, 2,
+            9, 4, 8,
+            2, 6, 3,
+          ],
+        },
+        {
+          diagonal: -4,
+        },
+    );
+  });
+
   it('triangular upper=false', function() {
     testTriangular(
         {
@@ -130,6 +178,31 @@ describe('test triangular', function() {
     );
   });
 
+  it('triangular fully copied upper=false diagonal=4 ', function() {
+    testTriangular(
+        {
+          shape: [3, 3],
+          data: [
+            7, 1, 2,
+            9, 4, 8,
+            2, 6, 3,
+          ],
+        },
+        {
+          shape: [3, 3],
+          data: [
+            7, 1, 2,
+            9, 4, 8,
+            2, 6, 3,
+          ],
+        },
+        {
+          upper: false,
+          diagonal: 4,
+        },
+    );
+  });
+
   it('triangular upper=false diagonal=-1', function() {
     testTriangular(
         {
@@ -154,4 +227,29 @@ describe('test triangular', function() {
         },
     );
   });
+
+  it('triangular fully zero upper=false diagonal=-4', function() {
+    testTriangular(
+        {
+          shape: [3, 3],
+          data: [
+            7, 1, 2,
+            9, 4, 8,
+            2, 6, 3,
+          ],
+        },
+        {
+          shape: [3, 3],
+          data: [
+            0, 0, 0,
+            0, 0, 0,
+            0, 0, 0,
+          ],
+        },
+        {
+          upper: false,
+          diagonal: -4,
+        },
+    );
+  });
 });