Alternative splicing is a powerful mechanism present in eukaryotic cells to obtain a wide range of transcripts and protein isoforms from a relatively small number of genes. The mechanisms regulating (alternative) splicing and the paradigm of consecutive splicing have recently been challenged, especially for genes with a large number of introns. RNA-Seq, a powerful technology using deep sequencing in order to determine transcript structure and expression levels, is usually performed on mature mRNA, therefore not allowing detailed analysis of splicing progression. Sequencing pre-mRNA at different stages of splicing potentially provides insight into mRNA maturation. Although the number of tools that analyze total and cytoplasmic RNA in order to elucidate the transcriptome composition is rapidly growing, there are no tools specifically designed for the analysis of nuclear RNA (which contains mixtures of pre- and mature mRNA). We developed dedicated algorithms to investigate the splicing process. In this paper, we present a new classification of RNA-Seq reads based on three major stages of splicing: pre-, intermediate- and post-splicing. Applying this novel classification we demonstrate the possibility to analyze the order of splicing. Furthermore, we uncover the potential to investigate the multi-step nature of splicing, assessing various types of recursive splicing events. We provide the data that gives biological insight into the order of splicing, show that non-sequential splicing of certain introns is reproducible and coinciding in multiple cell lines. We validated our observations with independent experimental technologies and showed the reliability of our method. The pipeline, named SplicePie, is freely available at: https://github.com/pulyakhina/splicing_analysis_pipeline. The example data can be found at: https://barmsijs.lumc.nl/HG/irina/example_data.tar.gz.