An algorithm described by Graybill (1969) factors a population correlation matrix, R, into an upper and lower triangular matrix, T and T', such that R = T'T. The matrix T is used to generate multivariate data sets from a multinormal distribution. When this algorithm is used to generate data for nonnormal distributions, however, the sample correlations are systematically biased downward. We describe an iterative technique that removes this bias by adjusting the initial correlation matrix, R, factored by the Graybill algorithm. The method is illustrated by simulating a multivariate study by Mihal and Barrett (1976). Large-N simulations indicate that the iterative technique works: multivariate data sets generated with this approach successfully model both the univariate distributions of the individual variables and their multivariate structure (as assessed by intercorrelation and regression analyses).A technique reviewed by Graybill (1969) can be used to generate multivariate data sets from multinormal distributions. The technique is not appropriate, however, for generating data sets from nonnormal multivariate distributions. Such distributions arise fairly often in the social sciences. Mihal and Barrett (1976), for example, reported data that clearly had nonnormal univariate distributions, as well as heterogeneous forms, across the eight variables in their study. Bradley (1993) was interested in generating multivariate data sets that would simulate the results of Mihal and Barrett's study as closely as possible. Two problems arose in the attempt to do this. First, since the distribution shapes used to model the variables had to be inferred from the descriptive statistics and scale limits reported by Mihal and Barrett (1976), the resulting distributions were approximate rather than exact. Second, when standard normal variables were correlated by the Graybill algorithm and then transformed to follow the desired nonnormal distributions, the intercorrelations were attenuated. This produced a systematic bias in the sample rs (see Table 6 in Bradley, 1993). In the present report, we attempt to solve both of these problems. The actual distribution shapes for the eight variables of Mihal and Barrett's study are ascertained by examining the raw data contained in Appendix A of Mihal's doctoral dissertation (Mihal, 1974), and the attenuation in the rs is eliminated by adjusting the values in the population correlation matrix to compensate for the effects of nonnormality.The computer simulations reported in this paper were conducted on a Macintosh IIci supplied by Apple Computer and the Consortium of Liberal Arts Colleges. The author also wishes to acknowledge the support of NSF-ILl Grant USE-8852l94, awarded to Bates College by the National Science foundation (G. Nigro and D. Bradley, principal investigators. Requests for reprints should be addressed to D. R. Bradley, Department of Psychology, Lewiston, ME 04240. Mihal and Barrett (1976) investigated the relationship between measures of cognitive style, reaction time (RT), s...