  The joint probability distribution function (PDF) of the height and its
gradients is derived for a zero tension $d+1$-dimensional Kardar-Parisi-Zhang
(KPZ) equation. It is proved that the height`s PDF of zero tension KPZ equation
shows lack of positivity after a finite time $t_{c}$. The properties of zero
tension KPZ equation and its differences with the case that it possess an
infinitesimal surface tension is discussed. Also potential relation between the
time scale $t_{c}$ and the singularity time scale $t_{c, \nu \to 0}$ of the KPZ
equation with an infinitesimal surface tension is investigated.
