Using the method of linearly independent polynomials, we derive an upper bound for the cardinality of a spherical s-distance set F where the sum of distinct inner products of any two elements from F is zero. Our result generalizes the well-known Gerzon’s bound for the cardinality of an equiangular spherical set to a significantly broader class of spherical s-distance sets. © 2022, Akadémiai Kiadó, Budapest, Hungary.