  We study the constraints on the CP-violating soft-breaking phases in the
minimal supersymmetric standard model using the limits on the chromoelectric
dipole moment of the strange quark extracted from the neutron EDM experiment.
Our investigation shows that the phase mediated by the gluino exchange diagram
has to be very small, $\phi\leq 8 10^{-4}$, for the common supersymmetric mass
of the order of 100 GeV. Then, solving the renormalization group equations
analytically by iterations, we calculate the electric dipole moment of the
neutron in the MSSM with CP-conserving soft-breaking parameters for the case of
three and four generations. For the three-generation case we resolve the
apparent discrepancies between order-of-magnitude estimates and numerical
calculations existing in the literature. In this case the EDM of the neutron
does not exceed $10^{-32} e cm$. For the four-generation case we show that
there is a significant enhancement which renders the EDM of the neutron at a
measurable level of $10^{-26}e cm$.
