TheVeselov’sdiscreteNeumannsystemisderivedthroughnonlinearizationofadiscretespectralproblem.BasedonthecommutativerelationbetweentheLaxmatrixandtheDarbouxmatrixwithfinitegenuspotentials,aspecialsolutioniscalculatedwiththehelpoftheBaker-Akhiezer-Kriecheverfunction.