Longitudinal or clustered response data arise in many applications such as, biostatistics, epidemiology and environmental studies. The repeated responses can not in general be assumed to be independent. The generalized estimating equations (GEE) approach is a widely used method to estimate marginal regression parameters for correlated responses. The advantage of the GEE is that the estimates of the regression parameters are asymptotically unbiased, although their small sample properties are not known. In this paper we review the GEE methodology for longitudinal binary data and propose a method of correcting bias of the estimates when the sample size is potentially small. Some simulation studies are provided to illustrate the theoretical results and applications of the GEE and its bias corrected version are also discussed to a set of environmental data.