RC4 algorithm is one of the most significant stream and symmetric cryptographic algorithms, it is simple and used in various commercial products, it has many weaknesses such as a bias in the key stream that some key bytes are biased toward some values. In this paper, a new algorithm is proposed by using initial state factorial to solve the correlation issue between public known outputs of the internal state by using an additional state table with the same length as that of the state to contain the factorial of initial state elements. The analysis of RC4 and developed RC4 algorithm is done based on their single bias and double byte bias and shows that many keystream output bytes of RC4 are produced key stream bytes that are biased to many linear combinations while developed RC4 key bytes have no single and double biases. The results show that the series that is generated by developed RC4 is more random than that generated by RC4 and the developed algorithm is faster than RC4 execution time and requires less time. Additionally, the developed algorithm is robust against many attacks such as distinguishing attack.