A new single-station model (SSM) for monthly median values of the ionospheric parameters foF2 and M(3000)F2 has been developed. Fourier analysis provides a tool for decomposing the time-varying ionospheric parameters. The 12-month smoothed sunspot number R12 was used as an external solar characteristic because of its availability and predictability. However, for the first time, the solar activity is described not only by R12, but also by the linear coefficient KR representing the tendency of the change of solar activity. A general non-linear approximation of the influence of the solar-cycle characteristics R12 and KR and ionospheric parameters foF2 and M(3000)F2 was accepted. The new SSM is applied to several European stations and its statistical evaluation shows better results than the other two SSMs used in the paper. The approach described in the paper does not contradict the use of different synthetic ionospheric indices (as the T-index, MF2-index); the basic aim is to show only that using one additional new characteristic of the solar-cycle variations, such as KR, improves the monthly median model.