S. Carpi et al. (Comm. Math. Phys., 402 (2023), 169–212) proved that every connected (i.e., haploid) Frobenius algebra in a tensor C ${}^{\ast }$-category is unitarizable (i.e., isomorphic to a special C ${}^{\ast }$-Frobenius algebra). Building on this result, we extend it to the non-connected case by showing that an algebra in a multitensor C ${}^{\ast }$-category is unitarizable if and only if it is separable.