Improvements to the Staniforth-Mitchell barotropic numerical weather prediction code are proposed. Three separate contributions are described: (1) a direct solution of the Helmholtz equation is offered as a substitute for the iterative scheme currently employed; (2) a new algorithm is developed to solve the generalized eigenvalue problem for symmetric tridiagonal matrices; (3) the latter algorithm is extended to deal with a periodic boundary condition. It is estimated that a direct solution of the Helmholtz equation, for a 13 X 13 grid, will effect a computation time saving per time step of at least 10 percent. FORTRAN 77 listings of the subroutines needed to implement the proposed improvements are included