In this technical note, we present an output feedback control for the cooperative robust output regulation problem of a class of heterogeneous minimum phase linear uncertain multi-agent systems with the arbitrary large plant uncertainty and the arbitrary nonidentical relative degrees. To estimate the system state, we propose a novel distributed observer that contains two distinct parts, where the first part is of the distributed form to estimate the regulated error, while the second part is a modified version of the standard reduced-order high-gain observer by replacing the regulated error with its estimation given in the first part. Our design significantly extends some current literatures in that it strictly removes the assumption of the identical relative degree, and hence applies to a much larger class of linear multi-agent systems.