Using Bony’s paramultiplication, we improve a previous backward uniqueness result for parabolic operators having coefficients non-Lipschitz continuous with respect to t but C2 with respect to x (see Del Santo and Prizzi in J. Math. Pures Appl. 84:471–491, 2005), showing that a similar result is valid when C2 regularity in x is replaced by Lipschitz regularity in x .
