  The scale invariant of the effective potential of the standard model at
two-loop is used as a boundary condition under the assumption that the two-loop
effective potential approximates the full effective potential. This condition
leads with the help of the renormalization group functions of the model at
two-loop to an algebraic equation of the scalar self coupling with coefficients
that depend on the gauge and the top quark couplings. It admits only two real
positive solutions. One of them, in the absence of the gauge and top quark
couplings, corresponds to the non-perturbative ultraviolet fixed point of the
scalar renormalization group function and the other corresponds to the
perturbative infrared fixed point. The dependence of the scalar coupling on the
top quark and the strong couplings at two-loop radiative corrections is
analyzed.
