RC4 has attracted many cryptologists due to its simple structure. In , Paterson, Poettering and Schuldt reported the results of a large scale computation of RC4 biases. Among the biases reported by them, we try to theoretically analyze a few which show very interesting visual patterns. We first study the bias which relates the key stream byte zi with i−k, where k is the first byte of the secret key. We then present a generalization of the Roos bias. In 1995, Roos observed the bias of initial bytes S[i] of the permutation after KSA towards fi=∑ir=1r+∑ir=0K[r]. Here we study the probability of S[i] equaling fy=∑yr=1r+∑yr=0K[r] for i≠y. Our generalization provides a complete correlation between zi and i−fy. We also analyze the key-keystream relation zi=fi−1 which was studied by Maitra and Paul  in FSE 2008. We provide more accurate formulas for the probability of both zi=i−fi and zi=fi−1 for different i’s than the existing works.