  We describe the twisted affine superalgebra $sl(2|2)^{(2)}$ and its quantized
version $U_q[sl(2|2)^{(2)}]$. We investigate the tensor product representation
of the 4-dimensional grade star representation for the fixed point
subsuperalgebra $U_q[osp(2|2)]$. We work out the tensor product decomposition
explicitly and find the decomposition is not completely reducible. Associated
with this 4-dimensional grade star representation we derive two $U_q[osp(2|2)]$
invariant R-matrices: one of them corresponds to $U_q[sl(2|2)^{(2)}]$ and the
other to $U_q[osp(2|2)^{(1)}]$. Using the R-matrix for $U_q[sl(2|2)^{(2)}]$, we
construct a new $U_q[osp(2|2)]$ invariant strongly correlated electronic model,
which is integrable in one dimension. Interestingly, this model reduces, in the
$q=1$ limit, to the one proposed by Essler et al which has a larger, $sl(2|2)$,
symmetry.
