diff --git a/src/cairo-matrix.c b/src/cairo-matrix.c
index f2be48b74..2ccae0ebd 100644
--- a/src/cairo-matrix.c
+++ b/src/cairo-matrix.c
@@ -728,6 +728,11 @@ _cairo_matrix_is_integer_translation (const cairo_matrix_t *matrix,
 
 #define SCALING_EPSILON _cairo_fixed_to_double(1)
 
+static cairo_bool_t
+within_scaling_epsilon(double a, double b) {
+    return fabs(a - b) < SCALING_EPSILON;
+}
+
 /* This only returns true if the matrix is 90 degree rotations or
  * flips. It appears calling code is relying on this. It will return
  * false for other rotations even if the scale is one. Approximations
@@ -737,21 +742,20 @@ _cairo_matrix_is_integer_translation (const cairo_matrix_t *matrix,
 cairo_bool_t
 _cairo_matrix_has_unity_scale (const cairo_matrix_t *matrix)
 {
-    /* check that the determinant is near +/-1 */
-    double det = _cairo_matrix_compute_determinant (matrix);
-    if (fabs (det * det - 1.0) < SCALING_EPSILON) {
-	/* check that one axis is close to zero */
-	if (fabs (matrix->xy) < SCALING_EPSILON  &&
-	    fabs (matrix->yx) < SCALING_EPSILON)
-	    return TRUE;
-	if (fabs (matrix->xx) < SCALING_EPSILON  &&
-	    fabs (matrix->yy) < SCALING_EPSILON)
-	    return TRUE;
-	/* If rotations are allowed then it must instead test for
-	 * orthogonality. This is xx*xy+yx*yy ~= 0.
-	 */
+    if (within_scaling_epsilon(matrix->xy, 0.0) && within_scaling_epsilon(matrix->yx, 0.0)) {
+	if (! (within_scaling_epsilon(matrix->xx, 1.0) || within_scaling_epsilon(matrix->xx, -1.0)))
+	    return FALSE;
+	if (! (within_scaling_epsilon(matrix->yy, 1.0) || within_scaling_epsilon(matrix->yy, -1.0)))
+	    return FALSE;
+    } else if (within_scaling_epsilon(matrix->xx, 0.0) && within_scaling_epsilon(matrix->yy, 0.0)) {
+	if (! (within_scaling_epsilon(matrix->xy, 1.0) || within_scaling_epsilon(matrix->xy, -1.0)))
+	    return FALSE;
+	if (! (within_scaling_epsilon(matrix->yx, 1.0) || within_scaling_epsilon(matrix->yx, -1.0)))
+	    return FALSE;
+    } else {
+	return FALSE;
     }
-    return FALSE;
+    return TRUE;
 }
 
 /* By pixel exact here, we mean a matrix that is composed only of
diff --git a/test/bug-927.c b/test/bug-927.c
new file mode 100644
index 000000000..85003f590
--- /dev/null
+++ b/test/bug-927.c
@@ -0,0 +1,58 @@
+/*
+ * Copyright © 2026 Uli Schlachter
+ *
+ * Permission is hereby granted, free of charge, to any person
+ * obtaining a copy of this software and associated documentation
+ * files (the "Software"), to deal in the Software without
+ * restriction, including without limitation the rights to use, copy,
+ * modify, merge, publish, distribute, sublicense, and/or sell copies
+ * of the Software, and to permit persons to whom the Software is
+ * furnished to do so, subject to the following conditions:
+ *
+ * The above copyright notice and this permission notice shall be
+ * included in all copies or substantial portions of the Software.
+ *
+ * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
+ * EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
+ * MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
+ * NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS
+ * BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN
+ * ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN
+ * CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+ * SOFTWARE.
+ */
+
+#include "cairo-test.h"
+
+static cairo_test_status_t
+draw (cairo_t *cr, int width, int height)
+{
+    double scale = 3;
+    cairo_matrix_t matrix = {
+	1 / scale, 0,
+	0, scale,
+	0, -100
+    };
+
+    cairo_set_line_width (cr, 20);
+    cairo_set_line_join (cr, CAIRO_LINE_JOIN_ROUND);
+
+    cairo_set_source_rgb (cr, 0, 0, 0);
+    cairo_paint (cr);
+
+    cairo_set_source_rgb (cr, 1, 1, 1);
+    cairo_set_matrix (cr, &matrix);
+    cairo_move_to (cr, -50, -50);
+    cairo_line_to (cr, 50, 50);
+    cairo_line_to (cr, 150, -50);
+    cairo_stroke (cr);
+
+    return CAIRO_TEST_SUCCESS;
+}
+
+CAIRO_TEST (bug_927,
+	    "Bug 927 (_cairo_matrix_has_unity_scale incorrectly returning true)",
+	    "matrix", /* keywords */
+	    NULL, /* requirements */
+	    30, 100,
+	    NULL, draw)
diff --git a/test/meson.build b/test/meson.build
index 3b460afc5..a543d5d75 100644
--- a/test/meson.build
+++ b/test/meson.build
@@ -30,6 +30,7 @@ test_sources = [
   'bug-431.c',
   'bug-448.c',
   'bug-535.c',
+  'bug-927.c',
   'bug-51910.c',
   'bug-75705.c',
   'bug-84115.c',
diff --git a/test/reference/bug-927.image16.ref.png b/test/reference/bug-927.image16.ref.png
new file mode 100644
index 000000000..c6f79441c
Binary files /dev/null and b/test/reference/bug-927.image16.ref.png differ
diff --git a/test/reference/bug-927.ps2.ref.png b/test/reference/bug-927.ps2.ref.png
new file mode 100644
index 000000000..1be717f15
Binary files /dev/null and b/test/reference/bug-927.ps2.ref.png differ
diff --git a/test/reference/bug-927.ps3.ref.png b/test/reference/bug-927.ps3.ref.png
new file mode 100644
index 000000000..1be717f15
Binary files /dev/null and b/test/reference/bug-927.ps3.ref.png differ
diff --git a/test/reference/bug-927.ref.png b/test/reference/bug-927.ref.png
new file mode 100644
index 000000000..81ece3565
Binary files /dev/null and b/test/reference/bug-927.ref.png differ
diff --git a/test/reference/bug-927.script.xfail.png b/test/reference/bug-927.script.xfail.png
new file mode 100644
index 000000000..4d8035eb3
Binary files /dev/null and b/test/reference/bug-927.script.xfail.png differ
diff --git a/test/reference/bug-927.svg11.xfail.png b/test/reference/bug-927.svg11.xfail.png
new file mode 100644
index 000000000..4d8035eb3
Binary files /dev/null and b/test/reference/bug-927.svg11.xfail.png differ