Abstract: To scale the error between the function implemented by one multi-valued neuron and its generalized spectrum,this paper defines the approximation error and gives the lower bound of it.By limiting the approximation error to 0,it also proposes the sufficient condition of the function implemented by a single multi-valued neuron,which is one of the measure indexes of the computational ability of a single multi-valued neuron.The lower bound of complexity of multi-valued neurons is obtained when the orthogonality condition of the function is not met.