I would like to introduce a way to iterate semiproper forcing. Suppose we have an initial segment, of limit length, of an iterated forcing. We consider the set of conditions that have sort of traceable countable stages. It turns out that this set of conditions forms a limit which sits between the direct and full limits. If we keep iterating semiproper p.o. sets under this limit, then every tail of the iteration is semiproper in the intermediate stage. In particular, the iteration itself is semiproper. This is a generalization of an iteration lemma on proper forcing under countable support.