diff --git a/Tests/test_file_bmp.py b/Tests/test_file_bmp.py
index 15b4b3670..bfe24e000 100644
--- a/Tests/test_file_bmp.py
+++ b/Tests/test_file_bmp.py
@@ -139,6 +139,13 @@ def test_rle8():
     with Image.open("Tests/images/hopper_rle8_row_overflow.bmp") as im:
         assert_image_similar_tofile(im.convert("RGB"), "Tests/images/hopper.bmp", 12)
 
+    # Signal end of bitmap before the image is finished
+    with open("Tests/images/bmp/g/pal8rle.bmp", "rb") as fp:
+        data = fp.read(1063) + b"\x01"
+        with Image.open(io.BytesIO(data)) as im:
+            with pytest.raises(ValueError):
+                im.load()
+
 
 def test_offset():
     # This image has been hexedited
diff --git a/src/PIL/BmpImagePlugin.py b/src/PIL/BmpImagePlugin.py
index 60617dce3..7221d7f06 100644
--- a/src/PIL/BmpImagePlugin.py
+++ b/src/PIL/BmpImagePlugin.py
@@ -282,7 +282,7 @@ class BmpRleDecoder(ImageFile.PyDecoder):
     def decode(self, buffer):
         data = bytearray()
         x = 0
-        while True:
+        while len(data) < self.state.xsize * self.state.ysize:
             num_pixels = self.fd.read(1)[0]
             byte = self.fd.read(1)
             if num_pixels: