The demonstration of repeated gamma-ray bursts from an individual source would severely constrain burst source models. Recent reports of evidence for repetition in the first BATSE burst catalog have generated renewed interest in this issue. Here, we analyze the angular distribution of 585 bursts of the second BATSE catalog (Meegan et al. 1994). We search for evidence of burst recurrence using the nearest and farthest neighbor statistic ad the two-point angular correlation function. We find the data to be consistent with the hypothesis that burst sources do not repeat; however, a repeater fraction of up to about 20% of the bursts cannot be excluded. Meegan, C. A. and Hartmann, D. H. and Brainerd, J. J. and Briggs, M. and Paciesas, W. S. and Pendleton, G. and Kouveliotou, C. and Fishman, G. and Blumenthal, G. and Brock, M. Marshall Space Flight Center NASA-TM-110835, NAS 1.15:110835 ...