A machine learning technique called Graph-Based Induction (GBI) extracts typical patterns from graph data by stepwise pair expansion (pairwise chunking). Because of its greedy search strategy, it is very efficient but suffers from incompleteness of search. Improvement is made on its search capability without imposing much computational complexity by 1) incorporating a beam search, 2) using a different evaluation function to extract patterns that are more discriminatory than those simply occurring frequently, and 3) adopting canonical labeling to enumerate identical patterns accurately. This new algorithm, now called Beam-wise GBI, B-GBI for short, was tested against a small DNA dataset from UCI repository and shown successful in extracting discriminatory substructures.