An efficient procedure for construction of the antisymmetric basis of j-shell states with isospin is presented. The basis is represented by one-particle coefficients of fractional parentage (CFPs) employing a simple enumeration scheme of many-particle states. The CFPs are those eigenvectors of the antisymmetrization operator matrix that correspond with unit eigenvalues. The approach is based on an efficient algorithm of construction of the idempotent matrix eigenvectors. The presented algorithm is faster than the diagonalization routine rs() from EISPACK for antisymmetrization procedure applications and is also amenable to parallel calculations.