Consistent biclusterings of sets of data are useful for solving feature selection and classification problems. The problem of finding a consistent biclustering can be formulated as a combinatorial optimization problem, and it can be solved by the employment of a recently proposed VNS-based heuristic. In this context, the concept of β-consistent biclustering has been introduced for dealing with noisy data and experimental errors. However, the given definition for β-consistent biclustering is coherent only when sets containing non-negative data are considered. This paper extends the definition of β-consistent biclustering to negative data and shows, through computational experiments, that the employment of the new definition allows to perform better classifications on a well-known test problem.