For the two dimensional Toda equation corresponding to the Kac-Moody algebra D_n⁽¹⁾, the Darboux transformation is constructed. The coefficient matrices of the Lax pair of this equation are of even order. Comparing with the scalars in the Darboux matrices for the two dimensional A_2l⁽²⁾, C_l⁽¹⁾ and D_l+1⁽²⁾ Toda equations, the structure of the 2x2 blocks in the Darboux matrix for this equation is much more complicated. In the construction of Darboux matrices, it is demanded that the solutions of the Lax pair are in Lag(C²ⁿ). With the help of a dense subset of Lag(C²ⁿ), the nontrivial blocks of the Darboux matrices are represented by elements of O(n,C). Quite a few algebraic techniques are used to simplify the Darboux matrices and to show that the form of the Darboux matrices only depends on the parity of n.