  We study the evolution under the renormalization group of the restrictions on
the parameters of the standard model coming from Non-Commutative Geometry,
namely $m_{top} = 2\,m_W$ and $m_{Higgs} = 3.14 \, m_W$. We adopt the point of
view that these relations are to be interpreted as {\it tree level} constraints
and, as such, can be implemented in a mass independent renormalization scheme
only at a given energy scale $\mu_0$. We show that the physical predictions on
the top and Higgs masses depend weakly on $\mu_0$.
