The convergence properties of popular nonlinear attitude estimators can be traced to the choice of an attitude error function. This paper considers a nonlinear deterministic direction cosine matrix estimator whose form is derived from an alternate attitude error function. While the resulting estimator shares several properties with those previously presented in the literature, the careful selection of an attitude error function results in an estimator with superior convergence properties. The attitude estimate is propagated using a rate gyroscope measurement and corrected using two or more vector measurements. Simulation and experimental results are presented that highlight the desirable properties of the proposed estimator.