Is the corneal reflex a cord-mediated reflex?

The corneal reflex may be elicited by lightly touching the cornea with a wisp of cotton; this sensory stimulus is transmitted by the first branch of the trigeminal nerve to the brainstem. There, thanks to connections of the trigeminal nerve with the facial (motor) nerve, a motor response occurs leading to contraction of the orbicularis oculi. The result is blinking or closing the eye on the same side. Thus this reflex is a brainstem and not a cord-mediated reflex.