In [5], the author gave a classification (with respect the group of invertible matrices) and a description of phase portraits of all planar homo- geneous quadratic systems x′ = P (x, y), y′ = Q(x, y). This classification is based on the number of integral lines (or singular points at infinity). The one that we propose makes more use of algebraic properties of polynomials P and Q (common factor, colinearity, . . . ) and produces less canonical forms. The tool used is Invariant Theory. The computing are made with Maple.