diff --git a/unix/syscall_unix_test.go b/unix/syscall_unix_test.go
index 0ecb5191..7d31402c 100644
--- a/unix/syscall_unix_test.go
+++ b/unix/syscall_unix_test.go
@@ -377,11 +377,11 @@ func TestRlimit(t *testing.T) {
 	}
 	set := rlimit
 	set.Cur = set.Max - 1
-	if runtime.GOOS == "darwin" && set.Cur > 10240 {
-		// The max file limit is 10240, even though
-		// the max returned by Getrlimit is 1<<63-1.
-		// This is OPEN_MAX in sys/syslimits.h.
-		set.Cur = 10240
+	if runtime.GOOS == "darwin" && set.Cur > 4096 {
+		// rlim_min for RLIMIT_NOFILE should be equal to
+		// or lower than kern.maxfilesperproc, which on
+		// some machines are 4096. See #40564.
+		set.Cur = 4096
 	}
 	err = unix.Setrlimit(unix.RLIMIT_NOFILE, &set)
 	if err != nil {
@@ -394,6 +394,9 @@ func TestRlimit(t *testing.T) {
 	}
 	set = rlimit
 	set.Cur = set.Max - 1
+	if runtime.GOOS == "darwin" && set.Cur > 4096 {
+		set.Cur = 4096
+	}
 	if set != get {
 		// Seems like Darwin requires some privilege to
 		// increase the soft limit of rlimit sandbox, though