Auxiliary fields in extended supersymmetry

A method is proposed for finding auxiliary fields for any massless linear chiral representation of $N$-extended supersymmetry with an arbitrary $N$. For each supermultiplet of free particles there exists a bilinear Lagrangian which is compatible with the supersymmetric quantization rules and is local with respect to the physical fields. The energy of the system of free fields is positive-definite.