  We find a new $4\times4$ solution to the $osp_q(1|2)$-invariant Yang-Baxter
equation with simple dependence on the spectral parameter and propose $2\times
2$ matrix expressions for the corresponding Lax operator. The general
inhomogeneous universal spectral-parameter dependent $R$-matrix is derived. It
is proven, that there are two independent solutions to the homogeneous
$osp_q(1|2)$-invariant YBE, defined on the fundamental three dimensional
representations. One of them is the particular case of the universal matrix,
while the second one does not admit generalization to the higher dimensional
cases. Also the $3 \times 3$ matrix expression of the Lax operator is found,
which have a well defined limit at $q \to 1$.
