In this paper we show some kind of isomorphism theorem for ordered sets under antiorders. Let $(X,=_X,\neq_X,\alpha)$ and $(Y,=_Y,\neq_Y,\beta)$ be ordered sets under antiorders, where the apartness $\neq_Y$ is tight. If $\varphi:X\longrightarrow Y$ reverse isotone strongly extensional mapping, then there exists a strongly extensional and embedding reverse isotone bijection \[ ((X,=_X,\neq_X,\alpha,c(R))/q,=_1,\neq_1,\gamma)\longrightarrow(Im(\varphi),=_Y,\neq_Y,\beta) \] where $c(R)$ is the biggest quasi-antiorder relation on $X$ under $R=\alpha\cap Coker(\varphi)$, $q=c(R)\cup c(R)^1$ and $\gamma$ is an antiorder induced by the quasiantiorder $c(R)$. If the condition $\alpha\cap\alpha_1=\emptyset$ holds, then the above bijection is isomorphism.