An efficient procedure for antisymmetrization of an arbitrary system of identical fermions is presented. The approach is based on a simple enumeration scheme for antisymmetric A-particle states and an efficient algorithm for calculation of the coefficients of fractional parentage (CFPs) for a single j-shell with isospin. The developed approach is implemented in a new procedure for the calculation of the electric quadrupole moment matrix elements of light atomic nuclei in the isospin formalism.