We have proposed more stable and accurate recursing equations and a computing procedure to calculate scattering coefficients for a multilayered sphere. The procedure involves three logarithmic derivatives of Ricatti-Bessel functions ψn′(z)/ ψn(z), χn′(z)/ χn(z), and ξn ′(z)/ξn (z), as well as the ratio ψn(z)/χn(z). The asymptotic behavior, stability, and accuracy of the procedure and scattering coefficients an and bn are discussed for any complex refractive indices. This procedure can be used for large and small inhomogeneous spherical particles.