The approximate unification of gauge couplings is the best indirect evidenc
e for low-energy supersymmetry, although it is not perfect in its simplest
realizations. Given the experimental evidence for small nonzero neutrino ma
sses, it is plausible to extend the MSSM with three right-handed neutrino c
hiral multiplets, with large Majorana masses below the unification scale, s
o that a seesaw mechanism can be implemented. In this extended MSSM, the un
ification prediction for the strong gauge coupling constant at M-L can be l
owered by up to similar to5%, bringing it closer to the experimental value
at 1 sigma, therefore improving significantly the accuracy of gauge couplin
g unification.