  In this paper, we present a method to construct new stable equivalences of
Morita type. Suppose that a stable equivalence of Morita type between finite
dimensional algebras $A$ and $B$ is defined by a $B$-$A$-bimodule $N$. Then,
for any finite admissible set $\Phi$ of natural numbers and any generator $X$
of the $A$-module category, the $\Phi$-Beilinson-Green algebras $\scr
G^{\Phi}_A(X)$ and $\scr G^{\Phi}_B(N\otimes_AX)$ are stably equivalent of
Morita type. In particular, if $\Phi=\{0\}$, we get a known result in
literature. As another consequence, we construct an infinite family of derived
equivalent algebras of the same dimension and of the same dominant dimension
such that they are pairwise not stably equivalent of Morita type. Finally, we
will prove that, if there is a graded stable equivalence of Morita type between
graded algebras, then we can get a stable equivalence of Morita type between
Beilinson-Green algebras associated with graded algebras
