The quadratic (Pfaffian) relations define a complete intersection variety Q in a ℙn of a-variables. In this procedure, we compute the loci of points in Q at which the rank of a-matrix drops, that is, the minimal primes of the maximal minors of the a-matrix (within the variety Q). These loci play an important role for the construction of numerical Godeaux surfaces with hyperelliptic fibers.