  We present results of a lattice computation of the matrix elements of the
vector and axial-vector currents which are relevant for the semi-leptonic
decays $D \rightarrow K$ and $D \rightarrow K^*$. The computations are
performed in the quenched approximation to lattice QCD on a $24^3 \times 48$
lattice at $\beta=6.2$ using an $O(a)$-improved fermionic action.
