In this paper we present analysis of the RC4 stream cipher and show that for each 2048-bit key there exists a family of related keys, differing in one of the byte positions. The keystreams generated by RC4 for a key and its related keys are substantially similar in the initial hundred bytes before diverging. RC4 is most commonly used with a 128-bit key repeated 16 times;this variant does not suffer from the weaknesses we describe. We recommend that applications of RC4 with keys longer than 128 bits (and particularly those using the full 2048-bit keys) discard the initial 256 bytes of the keystream output.