A loop transversal in a sharply 2-transitive permutation loop

The well-known theorem of M. Hall about the description of a finite sharply 2-transitive permutation group is generalized for the case of permutation loops. It is shown that the identity permutation with the set of all fixed-point-free permutations in a finite sharply 2-transitive permutation loop forms a loop transversal by its proper subloop – a stabilizator of one symbol.