With the increasing amount of available data and transformations manipulating the data, it has become essential to analyze and debug data transformations. A sub-problem of data transformation analysis is to understand why some data are not part of the result of a relational query. One possibility to explain the lack of data in a query result is to identify where in the query data pertinent to the expected, but missing output is lost during query processing. A first approach to this so called why-not provenance has been recently proposed, but we show that this first approach has some shortcomings. To overcome these shortcomings, we propose an algorithm to explain non-existing data in a query result. This algorithm allows to compute the why-not provenance for rela- tional queries involving selection, projection, join and union. After providing necessary definitions, this paper contributes a detailed description of the algorithm. A comparative evaluation shows that it is both more efficient and effective than the state-of-the-art ap- proach.