  We demonstrate that a system of bi-orthogonal polynomials and their
associated functions corresponding to a regular semi-classical weight on the
unit circle constitute a class of general classical solutions to the Garnier
systems by explicitly constructing its Hamiltonian formulation and showing that
it coincides with that of a Garnier system. Such systems can also be
characterised by recurrence relations of the discrete Painlev\'e type, for
example in the case with one free deformation variable the system was found to
be characterised by a solution to the discrete fifth Painlev\'e equation. Here
we derive the canonical forms of the multi-variable generalisation of the
discrete fifth Painlev\'e equation to the Garnier systems, i.e. for arbitrary
numbers of deformation variables.
