  Using the superspace formalism, we compute for the two-dimensional N=1
supersymmetric non-linear $\sigma$-model, the order $(\alpha^{\prime})^{2}$
$(R_{mnpq})^2$ (three-loop) correction to the central charge via the operator
product expansion of the supercurrent with itself. The contribution vanishes,
in agreement with previous results obtained from the usual $\sigma$-model
$\beta$-function approach.
