  Poly-Bernoulli numbers $B_n^{(k)}\in\mathbb{Q}$\,($n \geq 0$,\,$k \in
\mathbb{Z}$) are defined by Kaneko in 1997. Multi-Poly-Bernoulli
numbers\,$B_n^{(k_1,k_2,\ldots, k_r)}$, defined by using multiple
polylogarithms, are generations of Kaneko's Poly-Bernoulli
numbers\,$B_n^{(k)}$. We researched relations between Multi-Poly-Bernoulli
numbers and Poly-Bernoulli numbers of negative index in particular. In section
2, we introduce a identity for Multi-Poly-Bernoulli numbers of negative index
which was proved by Kamano. In section 3, as main results, we introduce some
relations between Multi-Poly-Bernoulli numbers and Poly-Bernoulli numbers of
negative index in particular.
