Parallel to what was done for the balanced model reduction version of the phase approximation problem (see Li and Jonckheere 1987), this paper provides anL∞bound on the phase approximation error when one-step-at-a-time optimal Hankel norm model reduction is used to reduce the stable projection of the phase function matrix. The one-step-at-a-time Hankel norm procedure allows for anL∞phase error bound twice as small as that of the balanced version.