A model of premixed lean Hydrogen-Oxygen flame is studied by singular perturbation techniques based on high activation energy. The model is built from four reaction steps consisting of two chain branching steps, a chain propagating step, and a recombination step. The analysis, in this case, gives rise to a layer phenomenon different from what is currently seen in combustion literature. First, there is a basic layer similar to those obtained for the one step reaction model. Then embedded in the first layer is a thinner layer giving rise to an interesting system of nonlinear boundary value problems. This system of nonlinear problems does not meet standard existence criterium and also involves an unknown parameter. Hence existence results are called for. Existence is proved for both the boundary value problem and the unknown parameter, and numerical solutions are obtained in support of the existence results. A numerical estimate of the unknown parameter is obtained. A generalization of the model for different reaction parameter ranges is made. Two new thin layers emerge. The structure of one of the new thin layers turns out to be exactly the same as that just described, hence the existence results do carry over. The boundary value problem resulting from the second of the new thin layers turned out to be quite simple and a solution could be written down explicitly.