Let A be a magic square of even order n.A is a Yang Hui type magic square with t-powered sum if for each e =2, 3, … , t, the sum of the elements of the first n/2 rows of A*e is the same as that of the last n/2 rows, and the sum of the elements of the left n2 columns of A*e is the same as that of the right n/2 columns, where A*e =(aie, j).A Yang Hui type magic square is a weak form of a t-multimagic square.In this report,a kind of strongly symmetric self-orthogonal diagonal Latin square is introduced and some constructions of Yang Hui type magic squares are presented based on strongly symmetric self-orthogonal diagonal Latin squares.Consequently, some families of Hui type magic squares are provided.