diff --git a/io/Makefile b/io/Makefile
index 19932d50f7..47666a1deb 100644
--- a/io/Makefile
+++ b/io/Makefile
@@ -188,6 +188,7 @@ tests := \
   tst-closefrom \
   tst-copy_file_range \
   tst-faccessat \
+  tst-fchmod-errors \
   tst-fchmodat \
   tst-fchownat \
   tst-fcntl \
diff --git a/io/tst-fchmod-errors.c b/io/tst-fchmod-errors.c
new file mode 100644
index 0000000000..ee15300fc3
--- /dev/null
+++ b/io/tst-fchmod-errors.c
@@ -0,0 +1,56 @@
+/* Test various fchmod error cases.
+   Copyright (C) 2024 Free Software Foundation, Inc.
+   This file is part of the GNU C Library.
+
+   The GNU C Library is free software; you can redistribute it and/or
+   modify it under the terms of the GNU Lesser General Public
+   License as published by the Free Software Foundation; either
+   version 2.1 of the License, or (at your option) any later version.
+
+   The GNU C Library is distributed in the hope that it will be useful,
+   but WITHOUT ANY WARRANTY; without even the implied warranty of
+   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+   Lesser General Public License for more details.
+
+   You should have received a copy of the GNU Lesser General Public
+   License along with the GNU C Library; if not, see
+   <https://www.gnu.org/licenses/>.  */
+
+#include <errno.h>
+#include <fcntl.h>
+#include <support/check.h>
+#include <support/xunistd.h>
+
+static int
+do_test (void)
+{
+  {
+    /* Permissions on /dev/null (the opened descriptor) cannot be changed.  */
+    int fd = xopen ("/dev/null", O_RDWR, 0);
+    errno = 0;
+    TEST_COMPARE (fchmod (fd, 0), -1);
+    TEST_COMPARE (errno, EPERM);
+    xclose (fd);
+
+    /* Now testing an invalid file descriptor.   */
+    errno = 0;
+    TEST_COMPARE (fchmod (fd, 0600), -1);
+    TEST_COMPARE (errno, EBADF);
+  }
+
+  errno = 0;
+  TEST_COMPARE (fchmod (-1, 0600), -1);
+  TEST_COMPARE (errno, EBADF);
+
+  errno = 0;
+  TEST_COMPARE (fchmod (AT_FDCWD, 0600), -1);
+  TEST_COMPARE (errno, EBADF);
+
+  /* Linux supports fchmod on pretty much all file descriptors, so
+     there is no check for failure on specific types of descriptors
+     here.  */
+
+  return 0;
+}
+
+#include <support/test-driver.c>