A modification of the usual perturbation expansion of the n-component O(n)-symmetric φ⁴ model, which leads to convergent series, is explicitly renormalized with an infinite set of counterterms. Renormal ization-group (RG) equations with only one coupling constant are derived and shown to govern the large-scale asymptotic behavior of the mode. A new expansion is constructed for the critical exponents η and v, which leads to numerical values in good agreement with Borel-transform based estimates and lattice results.