  We present a generalization of the hyperspherical harmonic formalism to study
systems made of quarks and antiquarks of the same flavor. This generalization
is based on the symmetrization of the $N-$body wave function with respect to
the symmetric group using the Barnea and Novoselsky algorithm. The formalism is
applied to study four-quark systems by means of a constituent quark model
successful in the description of the two- and three-quark systems. The results
are compared to those obtained by means of variational approaches. Our analysis
shows that four-quark systems with exotic $0^{+-}$ and non-exotic $2^{++}$
quantum numbers may be bound independently of the mass of the quark. $2^{+-}$
and $1^{+-}$ states become attractive only for larger mass of the quarks.
