  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.
${\bf 8}$ (1960), 277--286] and some more recent results of Del Santo and
Prizzi [J. Math. Pures Appl. ${\bf 84}$ (2005), 471--491; Ann. Mat. Pura Appl.,
to appear].
