Disjoint bilinear programming has appeared in miscellaneous practical applications. Although deterministic approaches such as cutting plane methods for solving it have been proposed, the frequently encountered computational problem regarding degeneracy still remains. This paper proposes a distance-following approach in order to generate a conservative hyperplane from a degenerate local star minimizer located by the augmented mountain climbing procedure, cut off it, and thus enable a cutting plane method to proceed without too much additional computational workload.