ELODIE.3.1 is an updated release of the library published in Prugniel & Soubiran (2001A&A...369.1048P, Cat. III/218; and 2004 version, in astro-ph/0409214). The library includes 1959 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: Teff from 3100K to 50000K, logg from -0.25 to 4.9 and [Fe/H] from -3 to +1. The library is given at two resolutions: R around 42000, with the flux normalized to the pseudo-continuum. A lower resolution version of the spectra (R around 10000), is 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 400nm 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