We present the analysis of the Blazhko effect - quasi-periodic modulation of pulsation amplitude and/or phase - in the Galactic bulge first overtone RR Lyrae stars (RRc). We used the data gathered during the fourth phase of the Optical Gravitational Lensing Experiment (OGLE). Out of 10826 analysed RRc stars, Blazhko effect was detected in 607 stars which constitute 5.6 per cent of the sample. It is the largest and most homogeneous sample of modulated RRc stars analysed so far. Modulation periods cover a wide range, from slightly above 2d to nearly 3000d. Multiperiodic modulation was detected in 47 stars. The appearance of modulation in the frequency domain was studied in detail. Modulation manifests either as close doublets or as equidistant triplets and multiplets centred on radial mode frequency and its harmonics. In a significant fraction (29 per cent) of stars, we have detected the modulation frequency itself, which corresponds to the modulation of the mean stellar brightness. Our search for period doubling effect, that was discovered recently in modulated fundamental mode RR Lyrae stars, and triggered development of new model behind the Blazhko modulation, yielded negative result. In 104 stars, we detected additional signals that could correspond to both radial and non-radial modes. Statistical properties of modulated stars were analysed in detail and confronted with properties of non-modulated stars and of modulated fundamental mode RR Lyrae stars. Our analysis provides constraints for the models to explain the Blazhko phenomenon, which still remains a puzzle more than hundred years after its discovery.