  We obtained BVIc photometry of IRC-10443 on 85 different nights distributed over two years, and in addition low resolution absolute spectro- photometry and high resolution Echelle spectroscopy. Our data show that IRC-10443, which was never studied before in any detail, is a SRa variable, characterized by Delta(B)=1.27, Delta(V)=1.14 and Delta(I)=0.70 mag amplitudes and mean values <B>=13.75, <V>=11.33 and <Ic>=6.18 mag. Two strong periodicities are simultaneously present: a principal one of 85.5 (+/-0.2) days, and a secondary one of 620 (+/-15) days, both sinusoidal in shape, and with semi-amplitudes Delta(V)=0.41 and 0.20 mag, respectively. IRC-10443 turns out to be a M7III star, with a mean heliocentric radial velocity -28 km/s and reddened by E(B-V)=0.87, a third of which of circumstellar origin. The same 0.5 kpc distance is derived from application of the appropriate period-luminosity relations to both the principal and the secondary periods. The long secondary period causes a sinusoidal variation in color of 0.13 mag semi-amplitude in V-Ic, with IRC-10443 being bluest at maximum and reddest at minimum, and with associated changes in effective temperature and radius of 85 K and 6%, respectively. This behavior of colors argues in favor of a pulsation nature for the still mysterious long secondary periods in AGB stars. 
IRC-10443: a multi-periodic SRa variable and the nature of long   secondary periods in AGB stars