The motion in the Maxwell orthogonal rheometer has been treated by several authors recently. The original purpose of this instrument was to measure the normal and shear stresses in a polymer melt being subjected to a shearing in three directions simultaneously. Later on, attempts were made to relate the experiment to the material constants of a nonlinear Maxwell model and an empirical model. The purpose of this article is two fold: to show that the steady motion in this rheometer is a motion with constant stretch history, and then to determine the five material functions for the general simple fluid if it were used in the rheometer. It is found that a close relation exists between these five material functions and the viscometric functions. The BKZ model is used to compute the stresses for this flow. The relation between the measured forces in the rheometer and the material functions is pointed out, and it is shown that this rheometer can be used to determine whether the fluid being sheared is a simple fluid with fading memory or not. In the Appendix it is shown that for the BKZ model, the memory functions determined from viscometric flows can be used to calculate the present five functions at low shear rates.