  In the present paper, we introduce a new family of $
  \theta-$methods for solving delay differential equations. New methods are
developed using a combination of decomposition technique viz. new iterative
method proposed by Daftardar Gejji and Jafari and existing implicit numerical
methods. Using Butcher tableau, we observed that new methods are non
Runge-Kutta methods. Further, convergence of new methods is investigated along
with its stability analysis. Applications to variety of problems indicates that
the proposed family of methods is more efficient than existing methods.
