Cotranslationally removes the N-terminal methionine from nascent proteins. The N-terminal methionine is often cleaved when the second residue in the primary sequence is small and uncharged (Met- Ala-, Cys, Gly, Pro, Ser, Thr, or Val). Required for normal progression through the cell cycle. {ECO:0000269|PubMed:16274222, ECO:0000269|PubMed:17114291}. This is the function of METAP1 (methionyl aminopeptidase 1, Ensembl gene identifier ENSG00000164024).