In this paper we study the backward uniqueness for parabolic equations with non- Lipschitz coefficients in time and space. The result presented here improves an old uniqueness theorem due to Lions and Malgrange [Math. Scand. 8 (1960), 277–286] and some more recent results of Del Santo and Prizzi [J. Math. Pures Appl. (9) 84 (2005), 471–491; Ann. Mat. Pura Appl. (4) 194 (2015), 387–403].
