Taguchi Immune Algorithm (TIA) is based on both features of the biological immune system and the Taguchi method which increases the ability of the Immune Algorithm (IA) to find the global optimal solution in a nonlinear space. In the TIA, the clonal proliferation within hypermutation for several antibody diversifications and the recombination by using the Taguchi method for the local search are integrated to improve the capabilities of exploration and exploitation. Two major tools are used in the Taguchi method; namely the Orthogonal Arrays (OAs) and the Signal to Noise Ratio (SNR). The effect of selecting the number of levels adopted in the construction of OAs on TIA is not studied before. So, this paper addresses the problem increasing the convergence speed of immune algorithm based two-dimensional recursive digital filters design process by adopting two, three and four levels OAs. For seek of comparison, the same computational experiments adopted in [1] are considered. Numerical results show that increasing the number of OA levels yields to faster convergence and better antibody genes selection in order to achieve the potential recombination, and consequently enhance the design process.