The now well-established L2 techniques applied to the description of the electronic continuum of small molecules and generally implemented with suitable oscillating basis sets are here adapted and used in connection with Gaussian type orbital (GTO) functions. As a test, a K-matrix approach associated with extended sets of GTOs is employed to compute with satisfactory accuracy partial wave phase shifts and both the integral and differential photoionization cross sections of the hydrogen molecule. It is apparently possible to greatly extend the range of applicability of the usual L2 techniques beyond the limited set of molecular systems amenable to the one center expansion approximation.