Context. Icy dwarf planets are key for studying the chemical and physical states of ices in the outer solar system. The study of secular and rotational variations gives us hints of the processes that contribute to the evolution of their surface. Aims: The aim of this work is to search for rotational variability on the surface composition of the dwarf planet (136472) Makemake Methods: We observed Makemake in April 2008 with the medium-resolution spectrograph ISIS, at the William Herschel Telescope (La Palma, Spain) and obtained a set of spectra in the 0.28-0.52 μm and 0.70-0.95 μm ranges, covering 82% of its rotational period. For the rotational analysis, we organized the spectra in four different sets corresponding to different rotational phases, and after discarding one with low signal to noise, we analyzed three of them that cover 71% of the surface. For these spectra we computed the spectral slope and compared the observed spectral bands of methane ice with reflectances of pure methane ice to search for shifts of the center of the bands, related to the presence of CH4/N2 solid solution. Results: All the spectra have a red color with spectral slopes between 20%/1000 Å and 32%/1000 Å in accordance with previously reported values. Some variation in the spectral slope is detected, pointing to the possibility of a variation in the surface content or the particle size of the solid organic compound. The absorption bands of methane ice present a shift toward shorter wavelengths, indicating that methane (at least partially) is in solid solution with nitrogen. There is no variation within the errors of the shifts with the wavelength or with the depth of the bands, so there is no evidence of variation in the CH4/N2 mixing ratio with rotation. By comparing with all the available data in the literature, no secular compositional variations between 2005 and 2008 is found.