  We show the existence and uniqueness of a continuous viscosity solution of a
system of partial differential equations (PDEs for short) without assuming the
usual monotonicity conditions on the driver function as in Hamad\`ene and
Morlais's article \cite{hamadene2013viscosity}. Our method strongly relies on
the link between PDEs and reflected backward stochastic differential equations
with interconnected obstacles for which we already know that the solution
exists and is unique for general drivers.
