  A class of bilinear permutation polynomials over a finite field of
characteristic 2 was constructed in a recursive manner recently which involved
some other constructions as special cases. We determine the compositional
inverses of them based on a direct sum decomposition of the finite field. The
result generalizes that in [R.S. Coulter, M. Henderson, The compositional
inverse of a class of permutation polynomials over a finite field, Bull.
Austral. Math. Soc. 65 (2002) 521-526].
