Some constants, which are needed for the principal realization of the basic representation are computed in the case of the affine Kac-Moody algebra \(D_n^{(1)}\). Assume \(S\) to be a suitable chosen central subalgebra of dimension \(n\) and let \(T_1,\ldots,T_n\) denote a normalized basis of \(S\), let \(A_1,\ldots,A_n\) be root vectors with respect to \(S\), then the constants in question are the roots \(\lambda_{rs}\) defined by the relations \([T_s,A_r] = \lambda_{rs}A_r\).