We present analytical constraints so that the wide class of color-char
ge-breaking (CCB) vacua is absent in the minimal supersymmetric standa
rd model (MSSM). We show that equal-scalar-field direction minima, whi
ch can be excluded by the well-known constraint like A(2) < 3(m(2)(2)
+ m(Q)(2) + m(U)(2)), are unstable with respect to small deviations fr
om the equal-field direction in the sfermion-Higgs interaction part of
the scalar potential. It is shown that a more severe constraint, roug
hly A < max(i) m(i), should be imposed to avoid the false CCB vacuum.