We report the discovery of amplitude and phase modulations typical of the Blazhko effect in 22 RRc and nine RRab type RR Lyrae stars in NGC 5024 (M53). This brings the confirmed Blazhko variables in this cluster to 23 RRc and 11 RRab stars, which represent 66 and 37 per cent of the total population of RRc and RRab stars in the cluster, respectively, making NGC 5024 the globular cluster with the largest presently known population of Blazhko RRc stars. We place a lower limit of 52 per cent on the overall incidence rate of the Blazhko effect among the RR Lyrae population in this cluster. New data have allowed us to refine the pulsation periods. The limitations imposed by the time span and sampling of our data prevent reliable estimations of the modulation periods. The amplitudes of the modulations range between 0.02 and 0.39mag. The RRab and RRc are neatly separated in the colour-magnitude diagram, and the RRc Blazhko variables are on average redder than their stable counterparts; these two facts may support the hypothesis that the horizontal branch (HB) evolution in this cluster is towards the red and that the Blazhko modulations in the RRc stars are connected with the pulsation mode switch.