Relating to the crucial problem of branch switching, the calculation of codimension 2 bifurcation points
is one of the major issues in numerical bifurcation analysis. In this paper, we focus on the double Hopf points for
delay differential equations and analyze in detail the corresponding eigenspace, which enable us to obtain the finite
dimensional defining system of equations of such points, instead of an infinite dimensional one that happens naturally
for delay systems. We show that the double Hopf point, together with the corresponding eigenvalues, eigenvectors
and the critical values of the bifurcation parameters, is a regular solution of the finite dimensional defining system
of equations, and thus can be obtained numerically through applying the classical iterative methods. We show our
theoretical findings by a numerical example.