A method of conjugate directions, the projection method, for solving unconstrained minimization problems is presented. Under the assumption of uniform strict convexity, the method is shown to converge to the global minimizer of the unconstrained problem and to have an (n − 1)-step superlinear rate of convergence. With a Lipschitz condition on the second derivatives, the rate of convergence is shown to be a modifiedn-step quadratic one.