  In the SU(5)/SO(5) little Higgs models radiative corrections give rise to the
SU(2)_L x U(1)_Y symmetry breaking. In this work we start a program for a
detailed determination of the relevant terms of the Higgs effective potential
by computing the contribution of the b, t and T quarks at the one-loop level,
as an starting point for higher-loops computation. In spite of the fact that
some two-loop level contributions are well known to be important, we use our
preliminary one-loop result to illustrate that, by demanding the effective
potential to reproduce exactly the Standard Model Higgs potential, and in
particular the relation m_H^2= 2 lambda v^2= 2 mu^2, it will be possible to set
new constraints on the parameter space of the Littlest Higgs model when the
computation of all the relevant contributions to the Higgs effective potential
is completed.
