It is very clear from many literature that the traditional methods for solving any quadratic programming problem including that of Lemke is basically tableau transformation were a new tableau is generated from the immediate preceding one by series of elementary tableau transformation where the entering variable is the minimum value chosen from the minimum ratio test criterion. This we noticed tend to worsen the problem of round off error especially in this modern age were information are easily assessed through computer. 

In this paper we modify Lemke algorithm by introducing the matrix algebra approach instead of the usual tableau transformation to control the accuracy of the inverse of the Hessian matrix. This we observe actually check the problem of the round off error.