Multi-valued　functions　can　be　compute　by　multi-valued　neural　network.　In　order　to　use　linear　algebra　method　for　analysis　of　multi-valued　function,　this　paper　gives　the　spectral　representation　of　multi-valued　functions.　By　define　a　checksum　function　of　n　variables,　this　paper　gives　an　group　of　orthogonal　bases.　Any　multi-valued　function　in　GF(　p)pn　can　be　uniquely　represented　as　a　linear　combination　of　the　bases.　The　coefficients　are　the　correlations　of　the　multi-valued　function　and　the　bases.　All　the　coefficients　combine　the　generalized　spectrum　of　the　multi-valued　function.　For　a　multi-valued　function　that　can　be　realized　by　a　multi-valued　neuron,　it　is　computable　by　depth-2　polynomial-size　neural　networks.