The Newton-Raphson method is a basic technique in unconstrained minimization which exactly minimizes a quadratic, symmetric approximation to an objective function. Functions with some degree of asymmetry can be optimized more efficiently by exact minimization of asymmetric approximations. In this paper, a special separable convex asymmetric fourth degree function is proposed whose minimum can Vie found in a finite number of steps, despite the high degree of the approximation. The method may be regarded as a. quasi-Newton method with a few operations added to measure and correct for asymmetry.