Catalyzes uridine to pseudouridine isomerization (pseudouridylation) of different mitochondrial RNA substrates (PubMed:27974379, PubMed:28082677, PubMed:41136621). Acts on position 1397 in 16S mitochondrial ribosomal RNA (16S mt-rRNA) (PubMed:27974379, PubMed:41136621). This modification is required for the assembly of 16S mt-rRNA into a functional mitochondrial ribosome (PubMed:27974379). As a component of a functional protein-RNA module, consisting of RCC1L, NGRN, RPUSD3, RPUSD4, TRUB2, FASTKD2 and 16S mt-rRNA, controls 16S mt- rRNA abundance and is required for intra-mitochondrial translation (PubMed:27667664). Acts on position 39 in mitochondrial tRNA(Phe) (PubMed:28082677). Also catalyzes pseudouridylation of mRNAs in nucleus: acts as a regulator of pre-mRNA splicing by mediating pseudouridylation of pre-mRNAs at locations associated with alternatively spliced regions (PubMed:35051350). Pseudouridylation of pre-mRNAs near splice sites directly regulates mRNA splicing and mRNA 3'-end processing (PubMed:35051350). {ECO:0000269|PubMed:27667664, ECO:0000269|PubMed:27974379, ECO:0000269|PubMed:28082677, ECO:0000269|PubMed:35051350, ECO:0000269|PubMed:41136621}. This is the function of RPUSD4 (RNA pseudouridine synthase D4, ENSG00000165526).