VLBI observations of 3C 245 obtained at 10.7 GHz with the Mark III array at five epochs in 1981-1986 are reported. The data-reduction and model-fitting procedures are explained, and the results are presented in tables, graphs, and maps along with previously published data on 11 other superluminal sources. The central component of the quasar is found to have an apparent transverse velocity of (3.1 + or - 1.4) c/h, assuming H0 = 100h km/s Mpc and q0 = 0.5. From the apparent source orientation (based on R, variability, apparent curvature, and projected linear size) it is inferred that the apparent transverse velocity is anticorrelated with the angle to the line of sight, as predicted by relativistic-beaming models of superluminal motion.