We present ELODIE.3.1, an updated release of the library published in Prugniel & Soubiran (2001, 2004). The library includes 1962 spectra of 1388 stars obtained with the ELODIE spectrograph at the Observatoire de Haute-Provence 193cm telescope in the wavelength range 390 to 680 nm. It provides a wide coverage of atmospheric parameters : T_eff from 3100 K to 50000 K, log g from -0.25 to 4.9 and [Fe/H] from -3 to +1. The library is given at two resolutions: R~42000, with the flux normalized to the pseudo-continuum, FWHM=0.55Å (R~10000) calibrated in physical flux (reduced above earth atmosphere) with a broad-band photometric precision of 2.5% and narrow-band precision of 0.5%. In this new release the data-reduction (flux calibration, reconnection of the echelle orders) has been improved, and in particular the blue region, between 390 and 400 nm has been added. The FITS files for each spectra, and the measured atmospheric parameters are publicly available. See the ELODIE.3.1 page for more details: http://www.obs.u-bordeaux1.fr/m2a/soubiran/elodie_library.html