Gaussian elimination with partial pivoting is the most favored technique for solution of a system of linear algebraic equations. However, in the existing form, the algorithm requires the entire data before it can he implemented. In some applications, the data matrix is recursively augmented with new row and column vectors. Recomputing the entire solution from a scratch becomes expensive O(n4). We propose an order-recursive version of Gaussian elimination with complexity O(n3), to solve the recursively augmented system of equation. © 1996 IEEE.