diff --git a/Tests/images/input_bw_one_band.fpx b/Tests/images/input_bw_one_band.fpx
new file mode 100644
index 00000000000..9bdc53763fe
Binary files /dev/null and b/Tests/images/input_bw_one_band.fpx differ
diff --git a/Tests/images/input_bw_one_band.png b/Tests/images/input_bw_one_band.png
new file mode 100644
index 00000000000..6b4c1f37696
Binary files /dev/null and b/Tests/images/input_bw_one_band.png differ
diff --git a/Tests/test_file_fpx.py b/Tests/test_file_fpx.py
index 818565f88b3..fa22e90f660 100644
--- a/Tests/test_file_fpx.py
+++ b/Tests/test_file_fpx.py
@@ -2,11 +2,22 @@
 
 from PIL import Image
 
+from .helper import assert_image_equal_tofile
+
 FpxImagePlugin = pytest.importorskip(
     "PIL.FpxImagePlugin", reason="olefile not installed"
 )
 
 
+def test_sanity():
+    with Image.open("Tests/images/input_bw_one_band.fpx") as im:
+        assert im.mode == "L"
+        assert im.size == (70, 46)
+        assert im.format == "FPX"
+
+        assert_image_equal_tofile(im, "Tests/images/input_bw_one_band.png")
+
+
 def test_invalid_file():
     # Test an invalid OLE file
     invalid_file = "Tests/images/flower.jpg"
diff --git a/src/PIL/FpxImagePlugin.py b/src/PIL/FpxImagePlugin.py
index f955b234769..a55376d0e08 100644
--- a/src/PIL/FpxImagePlugin.py
+++ b/src/PIL/FpxImagePlugin.py
@@ -154,13 +154,16 @@ def _open_subimage(self, index=1, subimage=0):
 
         for i in range(0, len(s), length):
 
+            x1 = min(xsize, x + xtile)
+            y1 = min(ysize, y + ytile)
+
             compression = i32(s, i + 8)
 
             if compression == 0:
                 self.tile.append(
                     (
                         "raw",
-                        (x, y, x + xtile, y + ytile),
+                        (x, y, x1, y1),
                         i32(s, i) + 28,
                         (self.rawmode,),
                     )
@@ -172,7 +175,7 @@ def _open_subimage(self, index=1, subimage=0):
                 self.tile.append(
                     (
                         "fill",
-                        (x, y, x + xtile, y + ytile),
+                        (x, y, x1, y1),
                         i32(s, i) + 28,
                         (self.rawmode, s[12:16]),
                     )
@@ -201,7 +204,7 @@ def _open_subimage(self, index=1, subimage=0):
                 self.tile.append(
                     (
                         "jpeg",
-                        (x, y, x + xtile, y + ytile),
+                        (x, y, x1, y1),
                         i32(s, i) + 28,
                         (rawmode, jpegmode),
                     )