For a multiple antenna Gaussian broadcast channel, we identify inputs that facilitate secure transmission between the intended communication parties in the presence of passive eavesdroppers. Assuming all channel information is known at the transmitter, we find that the optimization of Gaussian inputs for the general multiple antenna system is not convex and thus difficult to solve. However, the simpler case in which the intended receiver and the eavesdropper each use a single antenna is shown to be convex and the analytic solution is presented.