RC4 was designed in 1987 when 8-bit and 16-bit processors were commercially available. Today, most processors use 32-bit or 64-bit words but using original RC4 with 32/64 bits is infeasible due to the large memory constraints and the number of operations in the key scheduling algorithm. In this paper we propose a new 32/64-bit RC4-like keystream generator. The proposed generator produces 32 or 64 bits in each iteration and can be implemented in software with reasonable memory requirements. It has a huge internal state and offers higher resistance to state recovery attacks than the original 8-bit RC4. Further, on a 32-bit processor the generator is 3.1 times faster than original RC4. We also show that it can resist attacks that are successful on the original RC4. The generator is suitable for high speed software encryption.