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We use an improved Padé approximant to match between the Post Newtonian and Close Limit approximations of the outgoing gravitational wave radiation from a head-on binary black hole merger.  The traditional Padé approximant is improved by boundary conditions, thus allowing us to model the Post Newtonian (PN) approximation of the radiation in the Close Limit regime, where it currently breaks down. This technique allows us to recover the form of the Close Limit approximation of the radiation at small binary separation at low PN orders and allows us to recover the exact Close Limit approximation at unreasonably (>4PN) high PN orders. This work and the continuation of it may reduce the amount of costly, time-consuming numerical simulations needed to continue our understanding of binary black hole mergers.