In 2004, Bang-Jensen introduced Hi-free digraphs, for i in {1,2,3,4}, as a generalization of semicomplete and semicomplete bipartite digraphs. Bang-Jensen conjectured that an Hi-free digraph D, for i in {1,2,3,4}, is Hamiltonian if and only if D is strong and contains a cycle factor (that is, a collection of vertex disjoint cycles covering all the vertices of D). S. Wang and R. Wang proved the conjecture for i in {1,2} in 2009 and Galeana-Sánchez, Goldfeder and Urrutia proved the conjecture for i=3 in 2010. In this paper, we prove the conjecture for i=4.