The original Taylor distribution was designed to terminate abruptly in a pedestal (

) at its edges. It has been found recently, however, that a pedestal cannot be realized exactly in either the

or

planes, nor even approximately in the

plane. A new distribution is derived here that produces a Taylor pattern of order

and, hence, that vanishes linearly at the edges. This edge behavior can be realized exactly in the

plane and can be approximated as closely as desired in the

plane. All practical differences in operating performance between the two distributions have been found to be negligible.