Using the output from a univariate method-20 program (see Wingersky, Lees, Lennon, & Lord, 1969), the program BIV20 computes the estimated bivariate distribution of observed scores between two tests measuring the same psychological trait. The mathematics of these computations is briefly described in Appendix A. If desired, this estimated distribution is compared to an actual bivariate observed-score distribution provided by the user, and a chi-square between the estimated and actual distributions is computed. This program is written in Fortran IV for the IBM-7044 using the IBSYS operating system, Version 9, Level 10, modified to suppress underflow messages. Its only restriction is that the number of items on each test considered must be less than or equal to 50. It may be obtained, complete with instructions, from the authors.