In　this　paper,　we　study　the　cooperative　robust　output　regulation　problem　of　a　class　of　heterogeneous　minimum　phase　linear　uncertain　multi-agent　systems　with　the　arbitrary　nonidentical　relative　degree　via　the　output　feedback　control.　We　will　propose　a　novel　distributed　observer　to　estimate　the　system　state　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.　Comparing　with　some　current　literatures,　our　design　applies　to　a　much　larger　class　of　linear　multi-agent　systems.