A novel algorithm, called the edge determination algorithm, for exact computation of the frequency response of a linear interval system is proposed. The algorithm formulates candidate curves for the frequency response boundaries as cubic Bezier curves. The edge determination algorithm operates on the cubic Bezier control points of these curves to obtain those, or their parts, that are on the frequency response boundaries. It presents the frequency response boundaries as an array whose entries are the cubic Bezier control points of the curves on the boundaries. Examples for two different cases are presented to illustrate the mechanics and validity of the algorithm.