This paper presents a method for solving the eigenvalue problem Ax = lambdaBx, where A and B are real symmetric but not necessarily positive definite matrices, and B is nonsingular. The method reduces the general case into a form Cz = lambdaz where C is a pseudo-symmetric matrix. A further reduction of C produces a tridiagonal pseudo-symmetric form to which the interactive HR process is applied. The tridiagonal pseudo-symmetric form is invariant under the HR transformations. The amount of computation is significantly less than treating the problem by a general method.