  In this paper, we use cubic polynomials to approximate RR Lyrae light curves
and apply the method to HST data of RR Lyraes in the halo of M31. We compare
our method to the standard method of Fourier decomposition and find that the
method of cubic polynomials eliminates virtually all ringing effects and does
so with significantly fewer parameters than the Fourier technique. Further, for
RRc stars the parameters in the fit are all physical. Our study also reveals a
number of additional periodicites in this data not found previously: we find 23
RRc stars, 29 RRab stars and 3 multiperiodic stars.
