Approximating nonperiodic analytic functions with spectral accuracy is not an easy task. RBFs, just like polynomials and other pseudospectral methods, are susceptible to suffer from the Runge phenomenon, spurious oscillations near the edges of the domain, and from the ill-conditioning of the method’s associated system. Recently, Adcock et al have introduced a method which combines frames theory and Fourier extensions in [Adcock, Huybrechs, Martin- Vacquero, on the numerical stability of Fourier extensions, Found Comp Math 14, 635-687]. The method is not only spectrally convergent, it is also free from the Runge phenomenon even when the data is equispaced. We will use the fact that pseudospectral methods can be seen as particular cases of RBFs to construct an RBF-based frame method that generalized Adcocks Fourier extensions method.