Let G be a finite group. A subgroup H of G is called an ℋ-subgroup of G if NG(H) ∩ Hg ≤ H for all g ∈ G; G is said to be an ℋp-group if every cyclic subgroup of G of prime order or order 4 is an ℋ-subgroup of G. In this paper, the structure of the finite groups all of whose maximal subgroups of even order are ℋp-subgroups have been characterized.