Context.We perform a new spectroscopy of RR Lyrae to gain an understanding of the Blazhko effect. The Blazhko effect is a periodic amplitude and/or phase modulation shown by some RR Lyrae stars. Aims.New high precision spectroscopic observations of RR Lyrae, the brightest Blazhko star, were obtained continuously over an entire Blazhko period (41 days), from June to August 2000. This data set allows for a detailed analysis. Methods.We used Fourier techniques to analyze the metallic absorption line–profile variations over the pulsation and the Blazhko cycle. Results.This data set shows a triplet frequency structure with a large asymmetry in the modulation amplitudes. The right sidepeak amplitudes are higher than those on the left, and there is a linear decrease of the amplitudes of both right and left modulation components. The new data reveal that there is a very narrow interval in the pulsation cycle, 20% of the pulsation period, in which the modulation shows intense variations. The interval occurs during the phase of the main shock passage across the atmosphere of RR Lyrae. We detected no evidence whatsoever of a quintuplet structure within a median 1σ radial velocity uncertainty of 250 m/s. Our spectroscopic results make it more difficult to explain the Blazhko phenomenon with the current resonance models, which are the only theoretical models available that explain the Blazhko phenomenon, and give new insight for future Blazhko theoretical investigations.