Let a, b, c and d be functions in L2=L2(T, dq/2p), where T denotes the unit circle. Let P denote the set of all trigonometric polynomials. Suppose the singular INTEGRAL operators A and B are defined by A=aP+bQ and B=cP+dQ on P, where P is an analytic projection and Q=I-P is a co-analytic projection. In this paper, we use the Helson–Szego type set (HS)(r) to establish the condition of a, b, c and d satisfying ||Af||2³||Bf||2 for all f in P. If a, b, c and d are bounded measurable functions, then A and B are bounded operators, and this is equivalent to that B is majorized by A on L2, i.e., A*A³B*B on L2. Applications are then presented for the majorization of singular INTEGRAL operators on weighted L2 spaces, and for the normal singular INTEGRAL operators aP+bQ on L2 when a−b is a complex constant.