Abstract In [15] we obtained the Hyers–Ulam stability of the functional equation ∫ K ∫ G f ( x t k · y ) d μ ( t ) d k = f ( x ) g ( y ) , x , y ∈ G , $ \int _{K}\int _{G} f(xtk\cdot y)\,d\mu (t)\,dk=f(x)g(y), \quad x, y\in G, $ where G is a Hausdorff locally compact topological group, K is a compact subgroup of morphisms of G, μ is a K-invariant complex measure with compact support, provided that the continuous function f satisfies some Kannappan type condition. The purpose of this paper is to remove this restriction.