In Europe and North America, the most widely used stream cipher to ensure privacy and confidentiality of conversations in GSM mobile phones is the A5/1. In this paper, we present an improved guess-and-determine attack on the A5/1 stream cipher with an average time complexity of 2^48.5, which is much less than any known guess-and-determine attack. The attack has a 100% success rate and requires a small amount of memory. We provide a detailed description of our new attack along with its implementation results.