The sequence of monic Bessel polynomials is generated by the recurrence formula
with , and and depending on a (generally speaking, complex) parameter . The purpose of the author is to establish an explicit formula for an orthogonalizing weight, that is, for an absolutely continuous on function with rapid decay such that
Using the semi- classical character of the Bessel form, suitable formulations are obtained, although they are not proved for all values of the parameter . This generalizes the work of K. H. Kwon, S. S. Kim and S. S. Han [Bull. Lond. Math. Soc. 24, No. 4, 361-367 (1992; Zbl 0768.33007)], where the case of was studied.