The sign of an association measure between two variables may sometimes be reversed after marginalization over a confounder, called Simpson Paradox.Further a confounder may also make another paradox on a surrogate possible.Various criteria of surrogate have been proposed, such as the statistical surrogate (Prentice, 1989, Statist.Med.), the principal surrogate (Frangakis and Rubin, 2002, Biometrics), the strong surrogate (Lauritzen, 2004, Scand J Statist.).We illustrate that, with a surrogate endpoint defined by these criteria, it is possible that a treatmnt has a positive effect on the surrogate, which in turn has a positive effect on the true endpoint, but the treatment has a negative effect on the true endpoint, called a surrogate paradox (Chen, Geng and Jia, 2007, JRSSB).A consistent surrogate and a strictly consistent surrogate are proposed to avoid the surrogate paradox.We show the conditions for a consistent surrogate and a strictly consistent surrogate.