A parsimonious stepwise procedure for obtaining least squares solutions of multiple regression eqllntions when the regression coefficients are subject to arbitrary but consistent linear restraints is presented. The method is also applicable to the minimization of positive definite quadratic functions. Key to the method is the use of the elements of the appropriate inverse matrix for determining the standardized distance from any unrestricted, or conditionally unrestricted, solution to any boundary or boundary intersection of the permissible region for the regression coefficients.