Compact computational schemes for the first biharmonic problem in a rectangle (a \times b) with fourth- and second-order truncation errors and expressed in matrix form are presented. The matrix formulation of the fourth-order schemes is based on a kind of ((p, q, r, s)) noncoupled approach which may be viewed as an extension of the known non-coupled ((p, q)) method-see [6]-that uses 9 -point stencils to approximate the Laplacian at the (l: x m) interior nodes of a grid, with /and (m) standing for the number of equidistant subdivision points of the edens a and (b), respectively. The final matrix equation which serves as a fourth-order discrete equivalent of the problem may be expressed in conventional formulation as a symmetric system with (1 \times) m unknowns. For second-order schemes, the matrix equation in its initial form is based on the non-coupled ((p, q)) approach employing 5-point stencils to approximate the Laplacian at the (1 \times m) interior grid nodes, while the final system in its conventional formulation is again symmetric. For the specific values of (p), (q, r), and (s) used in this paper, namely (p=1, q=2, r=3), and (s=) 4 , it is possible to solve the problem by means of a quasi direct method after reducing the solution of both fourth- and second-order schemes to the solution of two symmetric and positive definite linear systems each of order equal to (\min (l, m)). In addition, for the same values of (p, q, r), and (s), the employment of the SOR iterarive method leads, after a reasonable number of iterations, to results which agree with the ones obtained by the already mentioned quasidirect method of solution. The experimentally observed accuracy for schemes with fourth-order truncation error (at least for the problems considered in this paper) was also of fourth order. For schemes with second-order truncation errors the observed accuracy was also of second order, as it should be, since the schemes in question express in effect the ((p, q)) approach for which-see ([5,7]-) a formal proof of accuracy exists. pit 1994 Academic Press, thc.