A twin tree consists of two trees $T_+$, $T_-$ together with a codistance function $T_+\times T_-\to\bold N_0$. Then $T_+$ and $T_-$ are semi-homogeneous of the same bidegree $(d_1,d_2)$; this means that $d_1$ and $d_2$ are the only valencies of vertices in $T_+$ (or $T_-$), occurring alternately at the vertices. The authors prove the following mean result: let $T_+$, $T_-$ be two semi-homogeneous trees. Then each semi-codistance function defined on subtrees $R_+$, $R_-$ of $T_+$, $T_-$ extends to a codistance function which makes $T_+$, $T_-$ into a twin tree. In particular, two trees $T_+$ and $T_-$ can be made into a twin tree if and only if $T_+$ and $T_-$ are both semi-homogeneous of the same bi-degree [cf. M. A. Ronan\ and J. Tits, Invent. Math. {\bf 116} (1994), no.~1-3, 463--479; MR1253201 (94k:20058)]. For another application, let $d_i\leq e_i$. Then every twin tree with bi-degree $(d_1,d_2)$ can be embedded into a twin tree with bi-degree $(e_1,e_2)$.