Using simple transformations of the block-diagram a criterion is derived for Instability (Zames 1964, 1966a, b) of conventional feedback systems with the non-linearity f(˙) satisfying an integral condition, namely,where β is a positive constant, It is shown that the criterion is more general than the Popov criterion (Popov 1962) in that a sector condition need not be satisfied and the non-linearity can lie in all the four quadrants. This is because the criterion fully exploits the characteristics of the open-loop transfer-function G(s). A more general case of the criterion with the non-linearity satisfying an integral plus a slope restriction is also presented.