Here we assume that the logarithmic asset price is given by a semimartingle. Jacod (2006) has derived an infeasible central limit theorem for the realized variance in such a general framework. However, here we focus on constructing a feasible limit theorem. We propose a new estimator for the asymptotic variance of the realized variance. This new estimator is based on generalized versions of the realized variance and the realized bipower variation. We prove the consistency of this estimator and can derive a feasible limit theorem for the realized variance.