miRNAs are small RNA molecules (' 22nt) that interact with their corresponding target mRNAs inhibiting the translation of the mRNA into proteins and cleaving the target mRNA. This second effect diminishes the overall expression of the target mRNA. Several miRNA-mRNA relationship databases have been deployed, most of them based on sequence complementarities. However, the number of false positives in these databases is large and they do not overlap completely. Recently, it has been proposed to combine expression measurement from both miRNA and mRNA and sequence based predictions to achieve more accurate relationships. In our work, we use LASSO regression with non-positive constraints to integrate both sources of information. LASSO enforces the sparseness of the solution and the non-positive constraints restrict the search of miRNA targets to those with down-regulation effects on the mRNA expression. We named this method TaLasso (miRNA-Target LASSO).We used TaLasso on two public datasets that have paired expression levels of human miRNAs and mRNAs. The top ranked interactions recovered by TaLasso are especially enriched (more than using any other algorithm) in experimentally validated targets. The functions of the genes with mRNA transcripts in the top-ranked interactions are meaningful. This is not the case using other algorithms.TaLasso is available as Matlab or R code. There is also a web-based tool for human miRNAs at http://talasso.cnb.csic.es/.