Let n ⩾ 4 be an even integer. Let K be a field with char K ≠ 2 and q an invertible element in K such that ∏ i = 1 n − 1 ( 1 + q i ) ≠ 0 . In this paper, we study the decomposition numbers over K of the Iwahori–Hecke algebra H q ( D n ) of type D n . We obtain some equalities which relate its decomposition numbers with certain Schur elements and the decomposition numbers of various Iwahori–Hecke algebras of type A with the same parameter q. When char K = 0 , this completely determine all of its decomposition numbers. The main tools we used are the Morita equivalence theorem established in [J. Hu, A Morita equivalence theorem for Hecke algebra H q ( D n ) when n is even, Manuscripta Math. 108 (2002) 409–430] and certain twining character formulae of Weyl modules over a tensor product of two q-Schur algebras.