diff --git a/src/display/canvas.js b/src/display/canvas.js
index ccca4e8545fad..d2dec4abbc8f9 100644
--- a/src/display/canvas.js
+++ b/src/display/canvas.js
@@ -2667,11 +2667,16 @@ const CanvasGraphics = (function CanvasGraphicsClosure() {
         const sqDet = (m[0] * m[3] - m[2] * m[1]) ** 2;
         const sqNorm1 = m[0] ** 2 + m[2] ** 2;
         const sqNorm2 = m[1] ** 2 + m[3] ** 2;
-        if (sqNorm1 !== sqNorm2 && sqNorm1 > sqDet && sqNorm2 > sqDet) {
-          // The parallelogram isn't a losange and both heights
-          // are lower than 1 so the resulting line width must be 1
+        if (sqNorm1 !== sqNorm2 && (sqNorm1 > sqDet || sqNorm2 > sqDet)) {
+          // The parallelogram isn't a losange and at least one height
+          // is lower than 1 so the resulting line width must be 1
           // but it cannot be achieved with one scale: when scaling a pixel
           // we'll get a rectangle (see issue #12295).
+          // For example with matrix [0.001 0, 0, 100], a pixel is transformed
+          // in a rectangle 0.001x100. If we just scale by 1000 (to have a 1)
+          // then we'll get a rectangle 1x1e5 which is wrong.
+          // In this case, we must reset the transform and set linewidth to 1
+          // and then stroke.
           this._cachedGetSinglePixelWidth = -1;
         } else if (sqDet > Number.EPSILON ** 2) {
           // The multiplication by the constant 1.0000001 is here to have
diff --git a/test/pdfs/.gitignore b/test/pdfs/.gitignore
index 29d3f5034466b..2c72de34bd1cb 100644
--- a/test/pdfs/.gitignore
+++ b/test/pdfs/.gitignore
@@ -94,6 +94,7 @@
 !issue11045.pdf
 !bug1057544.pdf
 !issue11150_reduced.pdf
+!issue6127.pdf
 !issue11242_reduced.pdf
 !issue11279.pdf
 !issue11362.pdf
diff --git a/test/pdfs/issue6127.pdf b/test/pdfs/issue6127.pdf
new file mode 100644
index 0000000000000..198d00cb698ae
Binary files /dev/null and b/test/pdfs/issue6127.pdf differ
diff --git a/test/test_manifest.json b/test/test_manifest.json
index 31b62fa6e22d9..55abbdfcb6b06 100644
--- a/test/test_manifest.json
+++ b/test/test_manifest.json
@@ -4877,6 +4877,13 @@
          }
        }
     },
+    {  "id": "issue6127",
+       "file": "pdfs/issue6127.pdf",
+       "md5": "65ef9572bddef5fddfaf7172f10a0df2",
+       "rounds": 1,
+       "lastPage": 1,
+       "type": "eq"
+    },
     {  "id": "annotation-polyline-polygon",
        "file": "pdfs/annotation-polyline-polygon.pdf",
        "md5": "e68611602f58c8ca70cc40575ba3b04e",