We study bi-parametric two-stage block group explicit (BGE) iteration method with the aid of nine-point compact sixth-order approximation for computing two-dimensional Helmholtz equation of elliptic nature. The exact Dirichlet boundary values are used and no fictitious points are required for computation. The error analysis is briefly discussed. The suggested BGE iteration method is compared with the corresponding BSOR method in two experiments, in terms of number of iterations required for convergence with optimal relaxation parameters. For computation, we use only a tridiagonal solver and CPU times are given in each calculation.