It is shown that a pxm transfer function G(s) with p⩾m can be decomposed as G = (I-νNΔN)-1...(I-νr+2Δr+2)-1 (I-νr=1Δr=1)-1GO where Δi are stable all-pass transfer functions, 1=ν1..=νr≫νr=1..≫νN≫0 are the Hankel-singular-values of GW*-1 where G*G=WW* with W stable and minimum phase. Results on the McMillan degree of GΛ:=(I-νiΔi)..(I-νNΔN)G then show that GΛ gives a good low order approximation to G in the sense of relative error.