We construct a pseudo-random generator for space bounded computations using the extractor of Zuckerman [7]. For machines that use S space and R < 2 ^1-ε random bits for ε Τ; 0, the generator uses a seed of length O((S log R)/ log S) which is shorter than the seed of both the generator of Nisan [4] and the generator of Nisan and Zuckerman[5]. We then use this generator to derandomize these machines in space which is better than the derandomization of [6].