A5/1 is the stream cipher algorithm used in GSM communication in order to provide over the air communication privacy. The objective of this paper is to modify the algorithm of the existing A5/1 stream cipher in order to improve the security of GSM communication. Several statistical tests such as frequency test, serial test, runs test, long runs of ones test, and linear complexity test were used to test the strength of the algorithm. Two proposed modified A5/1 algorithms successfully passed all the basic statistical tests.