This paper addresses the problem of false positive alarm when using a continuous air monitor (CAM) in decommissioning sites of nuclear facilities. CAMs are used to measure airborne activity and play an important role in the radiation protection of workers likely to be exposed to radioactive aerosols. Monitors usually sample aerosols on a membrane filter. Radioactive particles sampled are detected through the alpha and beta decays that they emit. These latter ionizing particles are measured online by spectrometry thanks to a Passivated Implanted Planar Silicon detector (PIPS). Alpha and beta decays, in this context, come mainly from the natural radon progeny (218Po, 214Pb, and so on) and, in the case of radioactive contamination, also from artificial radionuclides such as 239Pu or 137Cs. The aim of the CAM is to alert the workers when the artificial airborne activity occurs, always considering the presence of a variable background due to the natural particulate airborne activity. The CAM-specific algorithm considers this background dynamically and continuously, often by using a constant parameter. However, non-radioactive aerosols are also sampled on the membrane filter. These latter make the discrimination more difficult as they lead to the deterioration of the alpha-energy spectrum. In this paper, the effect of coarse non-radioactive aerosols on the CAM response is highlighted with four aerosol size-distributions. The evolution of the background is characterized as a function of the aerosol mass sampled, with the example of a simple algorithm. Thus, in this paper, results show a positive correlation of the background with the aerosol mass sampled by the CAM. In addition, results highlight at least two different evolutionary trends according to the aerosol size distribution. An explanation of these evolutions is given by considering the penetration profile of the natural radioactive aerosols in the granular deposit above the CAM filter. The main consequence of these results is that the background could not be considered as proportional to radon progeny as it is currently used.