  An algorithm for computing eigenvalues and eigenfunctions of the angular
spheroidal wave equation, based on a known but scarcely used method, is
developed. By requiring the regularity of the wave function, represented by its
series expansion, the eigenvalues appear as the zeros of a one variable
function easily computable. The iterative extended Newton method is suggested
as especially suitable for determining those zeros. The computation of the
eigenfunctions is then immediate. The usefulness of the method, applicable also
in the case of complex values of the "prolateness" parameter, is illustrated by
comparing its results with those of procedures used by other authors.
