Extended CCD monitoring of RR Gem revealed that it is a Blazhko type RRab star with the shortest Blazhko period (7.23d) and smallest modulation amplitude (delta_Mmax_<0.1mag) currently known. The short period of the modulation cycle enabled us to obtain complete phase coverage of the pulsation at each phase of the modulation. This is the first multicolour observation of a Blazhko star which is extended enough to define accurate mean magnitudes and colours of the variable at different Blazhko phases. Small, but real, changes in the intensity mean colours at different Blazhko phases have been detected. The Fourier analysis of the light curves shows that, in spite of the mmag and smaller order of the amplitudes, the triplet structure is noticeable up to about the 14th harmonic. The modulation is concentrated to a very narrow, 0.2 phase range of the pulsation, centred on the supposed onset of the H emission during rising light. These observational results raise further complications for theoretical explanation of the long known but poorly understood Blazhko phenomenon.