The author proves an identity of symmetry for the higher Bernoulli polynomials. It turns out implies that the recurrence relation and multiplication theorem for the Bernoulli polynomials discussed by F. T. Howard
[J. Number Theory 52, No. 1, 157–172 (1995; Zbl 0844.11019
)], as well as a relation of symmetry between the power sum polynomials and the Bernoulli numbers developed by H. J. H Tuenter
[Am. Math. Mon. 108, No. 3, 258–261 (2001; Zbl 0983.11008
)], are special cases of the results in this paper.