That rule is usually correct, but has some exceptions. Though 'between me' sounds better to my ear than 'between I'. Regardless, 'me' is always correct as the

That rule is usually correct, but has some exceptions. Though 'between me' sounds better to my ear than 'between I'. Regardless, 'me' is always correct as the object of a prepositional phrase because it's an object pronoun. 'I' is a subject pronoun.