Similarity join is a key operation in metric databases. It retrieves all pairs of elements that are similar. Solving such a problem usually requires comparing every pair of objects of the datasets, even when indexing and ad hoc algorithms are used. We propose a simple and efficient algorithm for the computation of the approximated k nearest neighbor self-similarity join. This algorithm computes $\Theta(3/2)$ distances and it is empirically shown that it reaches an empirical precision of 46% in real-world datasets. We provide a comparison to other common techniques such as Quickjoin and Locality-Sensitive Hashing and argue that our proposal has a better execution time and average precision.