Necessary de nitions can be found in [2, 5, 6]. De nition 1. Loop (Q;
) satisfying one of the equivalent identities x
yJx = y, xy
Jx = y, where J is a bijection of the set Q such that x
Jx = 1, is called a CI-loop [1]. De nition 2. Groupoid (Q;
) with the identity xy
Jrx = y, where Jr is a map of the set Q into itself, is called a left CI-groupoid [3, 4]. From the results of Keedwell and Shcherbacov [6, Proposition 3.28] it follows that the left CIgroupoid in which the map Jr is bijective, is a CI-quasigroup. Any nite left CI-groupoid is a quasigroup [4]. Theorem. Any left CI-groupoid (Q;
) is a CI-quasigroup.