We have suggested that the extension of SU (m|n) is to SU (l|m|n). We develop a local gauge theory of the graded algebra SU (l|m|n). We find the restrictions on the gauge potentials and matter fields in order that a physically suitable gauge invariant lag-rangian exists. It is natural to extend the graded algebra SU (2|1) electro weak model to include quarks in a superunified model.