smorodina is wrong, I'm afraid.From our own dictionary:
Between continues to be used to express relationship of persons or things considered individually, no matter how many.
(I believe you omitted the not from your sentence. I se this quite frequently from non-native spekaers, and occasionally from native speakers!)Thanks for your advice, however I am (not) fully convinced yet. I doubt if that rule is consistent. I have seen between being used with more than two.