A. vinculo matrimonii
(Latin) Divorced from marriage ties. A total divorce. A divorce a mensa et thoro is a partial divorce. The divorce a vinculo matrimonii is because the marriage was never legal, as in the case of bigamy, or marriage within the prohibited degrees; but a divorce a mensa et thoro is because the parties cannot live together from incompatibility of temper, in which case they may, if they choose, come together again.
Source: Dictionary of Phrase and Fable, E. Cobham Brewer, 1894
More on vinculo matrimonii from Infoplease: