  The aim of this paper is to provide an explicit basis of the miniversal
deformation of a monomial curve defined by a free semigroup -- these curves
make up a notable family of complete intersection monomial curves. First, we
dispense a general decomposition result of a basis of the miniversal
deformation of any complete intersection monomial curve. As a consequence, we
explicitly calculate this basis in the particular case of a monomial curve
defined from a free semigroup. This explicit computation yields some estimates
for the dimension of the moduli space of these family of curves.
