diff --git a/Tests/images/negative_height.j2k b/Tests/images/negative_height.j2k
new file mode 100644
index 00000000000..1dad43ae054
Binary files /dev/null and b/Tests/images/negative_height.j2k differ
diff --git a/Tests/test_file_jpeg2k.py b/Tests/test_file_jpeg2k.py
index 677a149810f..8f7d3f776c4 100644
--- a/Tests/test_file_jpeg2k.py
+++ b/Tests/test_file_jpeg2k.py
@@ -150,6 +150,11 @@ def test_reduce():
         assert im.size == (40, 30)
 
 
+def test_negative_height():
+    with Image.open("Tests/images/negative_height.j2k") as im:
+        assert im.size[1] == 0
+
+
 def test_load_dpi():
     with Image.open("Tests/images/test-card-lossless.jp2") as im:
         assert im.info["dpi"] == (71.9836, 71.9836)
diff --git a/src/PIL/Jpeg2KImagePlugin.py b/src/PIL/Jpeg2KImagePlugin.py
index c67d8d6bf60..2f946861f63 100644
--- a/src/PIL/Jpeg2KImagePlugin.py
+++ b/src/PIL/Jpeg2KImagePlugin.py
@@ -109,7 +109,7 @@ def _parse_codestream(fp):
     for i in range(csiz):
         ssiz[i], xrsiz[i], yrsiz[i] = struct.unpack_from(">BBB", siz, 36 + 3 * i)
 
-    size = (xsiz - xosiz, ysiz - yosiz)
+    size = (xsiz - xosiz, max(0, ysiz - yosiz))
     if csiz == 1:
         if (yrsiz[0] & 0x7F) > 8:
             mode = "I;16"