A thorough analysis of the multicolour CCD observations of the RRab-type variable, CZ Lacertae, is presented. The observations were carried out in two consecutive observing seasons in 2004 and 2005 within the framework of the Konkoly Blazhko Survey of bright, northern, short-period RRab variables. The O - C variation of CZ Lac indicated that a significant period decrease took place just around the time of the CCD observations. Our data gave a unique opportunity to study the related changes in the pulsation and modulation properties of a Blazhko star in detail. Two different period components (approximate to 14.6 and approximate to 18.6 d) of the Blazhko modulation were identified. Both modulation components had similar strength. The periods and amplitudes of the modulations changed significantly from the first season to the next, while the mean pulsation amplitude decreased slightly. The modulation frequencies were in a 5: 4 resonance ratio in the first observing season, and then the frequencies shifted in opposite directions, and their ratio was close to the 4: 3 resonance in the next season. The interaction of the two modulations caused beating with a period of 74 d in the first season, which resembled the 4-yr-long cycle of the approximate to 40-d modulation of RR Lyr. The mean values of the global physical parameters and their changes with the Blazhko phase of both modulation components were determined by the inverse photometric method.