Yearly averaging is a basic preprocessing of ionospheric data to smooth out the short-term, cyclic variations in the observations. However, we find that the use of yearly (running) average method probably leads to a biased evaluated relation between the ionospheric parameters (e.g., F2 peak electron density, NmF2) and the solar extreme ultraviolet (EUV) irradiance. The bias is essentially related to the annual/seasonal variations of the ionosphere, which means that the ionospheric sensitivity to the solar EUV irradiance varies with season and the same solar input can produce different ionization levels in different months/seasons. The yearly method simply averages the observations of different seasons, leading to a biased yearly NmF2-EUV relation, which will further affect the estimation of the ionospheric hysteresis (different NmF2-EUV relation in the solar rising and declining phase). Also, the extraction of long-term trends in the ionosphere will be more uncertain if using a regression approach based on the biased NmF2-EUV relation. In conclusion, we suggest to do the analysis month by month (using monthly average method) to properly deal with the annual/seasonal variations of the ionosphere, and to obtain accurate estimation of the hysteresis and long-term trends. Though both the yearly and monthly methods were used in precedent works, the bias introduced by the yearly average method has not been fully recognized prior to this study.