Context. Stellar kinematic groups are kinematically coherent groups of stars that might have a common origin. These groups spread through the Galaxy over time owing to tidal effects caused by Galactic rotation and disk heating. However, the chemical information survives these processes. Aims: The information provided by analysis of chemical elements can reveal the origin of these kinematic groups. Here we investigate the origin of the stars that belong to the Ursa Major (UMa) moving group (MG). Methods: We present high-resolution spectroscopic observations obtained from three different spectrographs of kinematically selected FGK stars of the Ursa Major moving group. Stellar atmospheric parameters (Teff, log g, ξ, and [Fe/H]) were determined using our own automatic code (StePar), which makes use of the sensitivity of iron equivalent widths (EWs) measured in the spectra. We critically compared the StePar results with other methods (Teff values derived using the infrared flux method (IRFM) and log g values based on Hipparcos parallaxes). We derived the chemical abundances of 20 elements and their [X/Fe] ratios for all stars in the sample. We performed a differential abundance analysis with respect to a reference star of the UMa MG (HD 115043). We also carried out a systematic comparison of the abundance pattern of the Ursa Major MG and the Hyades SC with the thin disk stellar abundances. Results: Our chemical tagging analysis indicates that the Ursa Major MG is less affected by field star contamination than other moving groups (such as the Hyades SC). We find a roughly solar iron composition [Fe/H] = 0.03 ± 0.07 dex for the finally selected stars, whereas the [X/Fe] ratios are roughly subsolar except for super-solar Barium abundance. Conclusions: We conclude that 29 out of 44 (i.e., 66%) candidate stars have similar chemical compositions. In addition, we find that the abundance pattern of the Ursa Major MG might be marginally different from that of the Hyades SC. Based on observations obtained with the HERMES spectrograph at the Observatorio del Roque de los Muchachos (La Palma), the FOCES spectrograph at Calar Alto, and with the Coudé-Échelle spectrograph of the Alfred-Jensch-Teleskop at the Thüringer Landessternwarte Tautenburg.The reduced spectra (FITS files) are only available at the CDS via anonymous ftp to http://cdsarc.u-strasbg.fr (http://130.79.128.5) or via http://cdsarc.u-strasbg.fr/viz-bin/qcat?J/A+A/597/A33