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The aim of this paper is to study the superstability problem of the d’Alembert type functional equation f(x+y+z)+f(x+y+σ(z))+f(x+σ(y)+z)+f(σ(x)+y+z)=4f(x)f(y)f(z) $$f(x+y+z)+f(x+y+\sigma (z\left)\right)+f(x+\sigma (y)+z)+f\left(\sigma \right(x)+y+z)=4f\left(x\right)f\left(y\right)f\left(z\right)$$ for all x, y, z ∈ G, where G is an abelian group and σ : G → G is an endomorphism such that σ(σ(x)) = x for an unknown function f from G into ℂ or into a commutative semisimple Banach algebra.