  The Wei-Norman technique allows to express the solution of a system of linear
non-autonomous differential equations in terms of product of exponentials. In
particular it enables to find a time-ordered product of exponentials by solving
a set of nonlinear differential equations. The method has numerous theoretical
and computational advantages, in particular in optimal control theory. We show
that in the unitary case, i.e.\ when the solution of the linear system is given
by a unitary evolution operator, the nonlinear system can be by an appropriate
choice of ordering reduced to a hierarchy of matrix Riccati equations. Our
findings have a particular significance in quantum control theory since pure
quantum evolution is unitary.
