Existence of normal bimagic squares

In this paper we provide a construction of normal bimagic squares by means of a magic pair of orthogonal general bimagic squares. It is shown that a normal bimagic square of order mnmn exists for all positive integers m,nm,n such that m,n∉{2,3,6}m,n∉{2,3,6} and m≡n(mod2), and a normal bimagic square of order 4m4m exists if and only if m≥2m≥2.