We investigate the convergence properties of the Iterated
Defect Correction (IDeC) method based on the
implicit Euler rule for the solution
of singular initial value problems with a singularity of the first kind.
We show that the method
retains its classical order of convergence which means that
the sequence of approximations obtained during the iteration
shows gradually growing order of convergence limited by
the smoothness of the data and technical
details of the procedure.