Pade-improvement of CP-odd Higgs decay rate into two gluons

We present an asymptotic Pade-approximant estimate for the four-loop coeffi cients within the linear combination of correlators entering the recently c alculated decay rate of a CP-odd Higgs boson, with an assumed mass m(A) = 1 00 GeV, into two gluons. All but one of these coefficients are shown to be determined for arbitrary mA from the known three-loop-order rate by renorma lization group methods. Asymptotic Pade-approximant estimates for these coe fficients are all seen to be within 12% of their correct values. The four-l oop term in the decay rate for m(A) = 100 GeV is estimated to be only 4.3% of its leading one-loop contribution.