Ulrich's (1984) proposal for simulating unit vectors from the von Mises-Fisher distribution is discussed and an alternative specification of the algorithm is given. Then we describe an application to the simulation of the von Mises-Fisher matrix distribution for rotations ofR3or,equivalently, the Bingham distribution on the unit sphere inR4The same idea also leadsto a procedure for simulating the Bingham distribution on the unit sphere inRqwhen q > 4.