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We show how the Implicit Regularization Technique (IRT) can be used for the perturbative renormalization of a simple field theoretical model generally used as a test theory for new techniques. While IRT has been applied successfully in many problems involving symmetry-breaking anomalies and nonabelian gauge groups, all at one-loop level, this is the first attempt at a generalization of the technique for perturbative renormalization. We show that the overlapping divergent loops can be given a completely algebraic treatment. We display the connection between renormalization and counterterms in the Lagrangian. The algebraic advantages make IRT worth studying for perturbative renormalization of gauge theories.

N-Loop Treatment of Overlapping Diagrams by the Implicit Regularization Technique