  An approximation algorithm is proposed to transform truncated QCD (or QED)
series for observables. The approximation is a modification of the Baker-Gammel
approximants, and is independent of the renormalization scale (RScl) $\mu$ --
the coupling parameter $\alpha(\mu)$ in the series and in the resulting
approximants can evolve according to the perturbative renormalization group
equation (RGE) to any chosen loop order. The proposed algorithm is a natural
generalization of the recently proposed method of diagonal Pad\'e approximants,
the latter making the result RScl-invariant in large-$\beta_0$ approximation
for ${\alpha}(\mu)$. The algorithm described below can extract large amount of
information from a calculated available truncated perturbative series for an
observable, by implicitly resumming large classes of diagrams.
