When the total angular momentum of a binary system Jtot=Jorb+Jspin is at a certain critical (minimum) value, a tidal instability occurs which eventually forces the stars to merge into a single, rapidly rotating object. The instability occurs when Jorb= 3Jspin, which in the case of contact binaries corresponds to a minimum mass ratio qmin≈ 0.071–0.078. The minimum mass ratio is obtained under the assumption that stellar radii are fixed and independent. This is not the case with contact binaries where, according to the Roche model, we have R2=R2(R1, a, q). By finding a new criterion for contact binaries, which arises from dJtot= 0, and assuming k21≠k22 for the component's dimensionless gyration radii, a theoretical lower limit qmin= 0.094–0.109 for overcontact degree f= 0–1 is obtained.