The paper is devoted to the study of robust strict positive realness design of interval systems, i.e. considering the question of designing a single controller which both robustly stabilizes an interval denominator system by unity feedback and makes the closed-loop transfer function robustly strictly positive real. By establishing a new computationally checkable criterion for the strict positive realness of a rational function, the extreme point result for a class of interval denominator systems is obtained, which significantly simplies the controller design procedure.