A new computational algorithm of Single-Term Walsh Series (STWS) for solving 2nth order state space equation representing the generalized linear, non-singular or singular, time varying system has been proposed. It is noticed from the literature that a second order (or third order) state space system (rxr matrix) is solved by converting into its first order (or second order) state space system resulting that the size of original system becomes doubled (2rx2r matrix) and the matrix to be inverted has its size drastically increased. In general, suppose that the problem of 2nth order state space system with r unknown dependent variables is to be solved by the method of second order state space formulation via STWS developed by others, then the size of the matrix to be inverted becomes (nrxnr). It is further noted that for a differential equations of (2n-1)th order with r unknown dependent variables, its order should, first be made as 2n by differentiating the differential equations of (2n-1)th order with respect to the independent variable and the resultant matrix to be inverted is of dimensions (nrxnr) in the case of second order state space formulation via STWS. In contrast to the technique mentioned above developed by others, the present numerical algorithm solves the given state space system with any order without converting into its lower order which in turn, implies that the original size of system matrix and the matrix to be inverted are not altered. So, the proposed new numerical algorithm is computationally very effective in lesser computing time as well as storage space.