  We present a set of exactly solvable Ising models, with half-odd-integer
spin-S on a square-type lattice including a quartic interaction term in the
Hamiltonian. The particular properties of the mixed lattice, associated with
mixed half-odd-integer spin-(S,1/2) and only nearest-neighbour interaction,
allow us to map this system either onto a purely spin-1/2 lattice or onto a
purely spin-S lattice. By imposing the condition that the mixed
half-odd-integer spin-(S,1/2) lattice must have an exact solution, we found a
set of exact solutions that satisfy the {\it free fermion} condition of the
eight vertex model. The number of solutions for a general half-odd-integer
spin-S is given by $S+1/2$. Therefore we conclude that this transformation is
equivalent to a simple spin transformation which is independent of the
coordination number.
