All Hamiltonian non-abelian Painlevé systems of P 1 - P 6 type with constant coefficients are found. For P 1 - P 5 systems, we replace an appropriate inessential constant parameter with a non-abelian constant. To prove the integrability of new P 3 ′ and P 5 systems thus obtained, we find isomonodromic Lax pairs for them.