  In this article, we study a special class of Jimbo-Miwa-Mori-Sato
isomonodromy equations, which can be seen as a higher-dimensional
generalization of Painlev\'e VI. We first construct its convergent $n\times n$
matrix series solutions satisfying certain boundary condition. We then use the
Riemann-Hilbert approach to prove that the resulting solutions are almost all
the solutions. Along the way, we find a shrinking phenomenon of the eigenvalues
of the submatrices of the generic matrix solutions in the long time behaviour.
