Institut fu¨r Theoretische Physik, Universit¨at Hannover, D-30167 Hannover, Germany(February 1, 2008)We study the distillability of a certain class of bipartitedensity operators which can be obtained via depolarizationstarting from an arbitrary one. Our results suggest that non-positivity of the partial transpose of a density operator is nota sufficient condition for distillability, when the dimension ofboth subsystems is higher than two.03.67.-a, 03.65.Bz, 03.65.Ca, 03.65.HkI. INTRODUCTION