Finger, Horn, and Mandula showed in a Tamm-Dancoff approximation in QCD that Coulomb exchange induces instability of the chiral-invariant vacuum for ..cap alpha../sub s/>..cap alpha../sub s//sup crit/ in the sense that for ..cap alpha../sub s/>..cap alpha../sub s//sup crit/ there are negative eigenvalues of an operator H derived by them. We show here that another critical coupling constant ..cap alpha../sub s//sup primecrit/>..cap alpha../sub s//sup crit/ is more meaningful. For ..cap alpha../sub s/>..cap alpha../sub s//sup primecrit/ there is no positive self-adjoint extension of H; for ..cap alpha../sub s/<..cap alpha../sub s//sup primecrit/ there is at least one; when ..cap alpha../sub s//sup crit/<..cap alpha../sub s/<..cap alpha../sub s//sup primecrit/, among several self-adjoint extensions, a positive one is singled out by the physical requirement of a finite kinetic-energy expectation value. Considering, respectively, Coulomb exchange with the Tamm-Dancoff approximation, Coulomb exchange with the Bogoliubov-Valatin approximation, and Coulomb exchange plus transverse-gluon exchange, the values are (4/3)..cap alpha../sub s//sup primecrit/ = 8..pi../(4+..pi.. /sup 2/), 4/..pi.., 12/5..pi.. to be compared with (4/3)..cap alpha../sub s//sup crit/ = (3/2), 1, ..pi../(3..pi..-4).