  A complete analysis of all the potentially dangerous directions in the
field-space of the minimal supersymmetric standard model is carried out. They
are of two types, the ones associated with the existence of charge and color
breaking minima in the potential deeper than the realistic minimum and the
directions in the field-space along which the potential becomes unbounded from
below. The corresponding new constraints on the parameter space are given in an
analytic form, representing a set of necessary and sufficient conditions to
avoid dangerous directions. They are very strong and, in fact, there are
extensive regions in the parameter space that become forbidden. This produces
important bounds, not only on the value of $A$, but also on the values of $B$
and $M_{1/2}$. Finally, the crucial issue of the one-loop corrections to the
scalar potential has been taken into account in a proper way.
