Let S = K[x1.xn] be a polynomial ring over a field K and I a homogeneous ideal in S generated by a regular sequence f1; f2, fk of homogeneous forms of degree d. We study a generalization of a result of Conca et al. [9] concerning Koszul property of the diagonal subalgebras associated to I. Each such subalgebra has the form K[(Ie)ed+c], where c; ε N. For k = 3, we extend [9, Corollary 6.10] by proving that K[(Ie))ed+c] is Koszul as soon as c ≥ d/2 and e > 0. We also extend [9, Corollary 6.10] in another direction by replacing the polynomial ring with a Koszul ring. © 2014 Rocky Mountain Mathematics Consortium.