  We prove that for two germs of analytic mappings $f,g\colon (\mathbb{C}^n,0)
\rightarrow (\mathbb{C}^p,0)$ with the same Newton polyhedra which are
(Khovanskii) non-degenerate and their zero sets are complete intersections with
isolated singularity at the origin, there is a piecewise analytic family
$\{f_t\}$ of analytic maps with $f_0=f, f_1=g$ which has a so-called {\it
uniform stable radius for the Milnor fibration}. As a corollary, we show that
their Milnor numbers are equal. Also, a formula for the Milnor number is given
in terms of the Newton polyhedra of the component functions. This is a
generalization of the result by C. Bivia-Ausina. Consequently, we obtain that
the Milnor number of a non-degenerate isolated complete intersection
singularity is an invariance of Newton boundaries.
