We study constraints among coupling constants of the standard model obtained
in the noncommutative geometry (NCG) method. First, we analyze the evolution of
the Higgs boson mass under the renormalization group by adopting the idea of
Álvarez et al. For this analysis we derive two certain constraints by
modifying Connes's way of constructing the standard model. Next, we find
renormalization group invariant (RGI) constraints in the NCG method. We also
consider the relation between the condition that a constraint among coupling
constants of a model becomes RGI and the condition that the model becomes
multiplicative renormalizable by using a simple example.