A protein complex that consists of a catalytic alpha subunit (alpha-MPP) and a regulatory beta subunit (beta-MPP), and catalyzes the release of N-terminal targeting peptides from precursor proteins imported into the mitochondrion. [ https://www.brenda-enzymes.info/enzyme.php?ecno=3.4.24.64 https://enzyme.expasy.org/EC/3.4.24.64 ]