One of the important problems that arise when investigating dynamics of Few-Body Nuclear systems within the framework of the Hyperspherical Function (HF) Method, is the problem of constructing wave functions that are antisymmetric under particle interchange. Parentage scheme of symmetrization (PSS) allows to construct N-body symmetrized HF from functions with arbitrary quantum numbers by the use of the transformation coefficients related with the permutations of last two particles. N-body HF corresponding to the representation of the N-particle permutation group were obtained for N=3,4,5,6 by finding parentage coefficients and constructing linear combinations of the N-particle functions corresponding to the irreducible representations of N-1 particle permutation
group . However, construction schemes for the fully anti-symmetric wave functions, consisting of spin and isospin parts along with the hyperspherical parts, has not been systematically addressed in the literature. Solution of this problem becomes sufficiently complex as number of particles increases. This article develops construction schemes for four particle wave functions that are anti-symmetric under particle interchange by building all possible combinations of spin, isospin, and hyperspherical parts.