diff --git a/Tests/test_image_quantize.py b/Tests/test_image_quantize.py
index 873a9bb5dcb..e1aa6252b7a 100644
--- a/Tests/test_image_quantize.py
+++ b/Tests/test_image_quantize.py
@@ -94,6 +94,19 @@ def test_quantize_dither_diff() -> None:
     assert dither.tobytes() != nodither.tobytes()
 
 
+@pytest.mark.parametrize(
+    "method", (Image.Quantize.MEDIANCUT, Image.Quantize.MAXCOVERAGE)
+)
+def test_quantize_kmeans(method) -> None:
+    im = hopper()
+    no_kmeans = im.quantize(kmeans=0, method=method)
+    kmeans = im.quantize(kmeans=1, method=method)
+    assert kmeans.tobytes() != no_kmeans.tobytes()
+
+    with pytest.raises(ValueError):
+        im.quantize(kmeans=-1, method=method)
+
+
 def test_colors() -> None:
     im = hopper()
     colors = 2
diff --git a/src/PIL/Image.py b/src/PIL/Image.py
index ac3a533211b..59c5c36f3b6 100644
--- a/src/PIL/Image.py
+++ b/src/PIL/Image.py
@@ -1141,7 +1141,7 @@ def quantize(
                        The exception to this is RGBA images. :data:`Quantize.MEDIANCUT`
                        and :data:`Quantize.MAXCOVERAGE` do not support RGBA images, so
                        :data:`Quantize.FASTOCTREE` is used by default instead.
-        :param kmeans: Integer
+        :param kmeans: Integer greater than or equal to zero.
         :param palette: Quantize to the palette of given
                         :py:class:`PIL.Image.Image`.
         :param dither: Dithering method, used when converting from
@@ -1184,6 +1184,10 @@ def quantize(
             new_im.palette = palette.palette.copy()
             return new_im
 
+        if kmeans < 0:
+            msg = "kmeans must not be negative"
+            raise ValueError(msg)
+
         im = self._new(self.im.quantize(colors, method, kmeans))
 
         from . import ImagePalette
diff --git a/src/libImaging/Quant.c b/src/libImaging/Quant.c
index 398fbf6db57..2582830c4a4 100644
--- a/src/libImaging/Quant.c
+++ b/src/libImaging/Quant.c
@@ -1471,7 +1471,7 @@ quantize(
     fflush(stdout);
     timer = clock();
 #endif
-    if (kmeans) {
+    if (kmeans > 0) {
         k_means(pixelData, nPixels, p, nPaletteEntries, qp, kmeans - 1);
     }
 #ifndef NO_OUTPUT
@@ -1627,7 +1627,7 @@ quantize2(
             pixelData, nPixels, p, nQuantPixels, avgDist, avgDistSortKey, qp)) {
         goto error_4;
     }
-    if (kmeans) {
+    if (kmeans > 0) {
         k_means(pixelData, nPixels, p, nQuantPixels, qp, kmeans - 1);
     }