The homoclinic orbit associated with the transition from steady convection to Chaos in the weak turbulent regime is difficult to recover in simple computational procedures because of its unstable nature. A simple procedure which recovers the homoclinic orbit up to the desired accuracy is presented. This procedure combines the insight obtained from previous work on a local non-linear analysis of the problem and the Adomian＇s decomposition method of solution which provides a global semi-analytical solution,