A recently developed inversion method for pentadiagonal matrices is reconsidered in this work. The mathematical structure of the previously suggested method is fully developed. In the process of establishing the mathematical structure, certain determinantial relations specific to pentadiagonal matrices were also established. This led to a rather general necessary and sufficient condition for the method to work. All the so called forward and backward leading principal submatrices need to be non-singular. While this condition sounds restrictive it really is not so. These are in fact the conditions for forward and backward Gauss Eliminations without any pivoting requirement. Additionally, the method is more effective computational complexity wise then recently published competitive methods.