The problem discussed in this paper deals with maximization (minimization) under linear restrictions, of a quadratic function of the form (1/2XtUX + VX) where U is negative (positive) semi definite. The optimum solution to this problem can be obtained by solving a certain enlarged system of equations representing the Kuhn-Tucker conditions. In this paper we will show that an equivalent system of equations of smaller dimensionality can be derived directly from any basic solution to the quadratic programming problem. We will also show that a variant of Wolfe's procedure for quadratic programming, which essentially uses the simplex method, can be used to solve this equivalent problem using a n × (2n + 1) tableau giving the optimum solution in a finite number of iterations. The procedure can be programmed on a computer with minor modifications to the code for linear programming.