HIGHER SPIN BRS COHOMOLOGY OF SUPERSYMMETRIC CHIRAL MATTER IN D=4

We examine the BRS cohomology of chiral matter in N = 1, D = 4 supersy mmetry to determine a general form of composite superfield operators w hich can suffer from supersymmetry anomalies. Composite superfield ope rators Psi((a,b)) are products of the elementary chiral superfields S and ($) over bar S and the derivative operators D-x, and ($) over bar D-beta and partial derivative(x beta). Such superfields Psi((a,b)) can be chosen to have ''a'' symmetrized undotted indices x(i) and ''b'' s ymmetrized dotted indices beta(j). The result derived here is that eac h composite superfield Psi((a,b)) is subject to potential supersymmetr y anomalies if a - b is an odd number, which means that Psi((a,b)) is a fermionic superfield.