Gene coexpression networks inferred by correlation from high-throughput profiling such as microarray data represent simple but effective structures for discovering and interpreting linear gene relationships. In recent years, several approaches have been proposed to tackle the problem of deciding when the resulting correlation values are statistically significant. This is most crucial when the number of samples is small, yielding a non-negligible chance that even high correlation values are due to random effects. Here we introduce a novel hard thresholding solution based on the assumption that a coexpression network inferred by randomly generated data is expected to be empty. The threshold is theoretically derived by means of an analytic approach and, as a deterministic independent null model, it depends only on the dimensions of the starting data matrix, with assumptions on the skewness of the data distribution compatible with the structure of gene expression levels data. We show, on synthetic and array datasets, that the proposed threshold is effective in eliminating all false positive links, with an offsetting cost in terms of false negative detected edges.