A new stellar library at the near-IR spectral region developed for the empirical calibration of the Caii triplet and stellar population synthesis modelling is presented. The library covers the range λλ8348-9020 at 1.5-Å (FWHM) spectral resolution, and consists of 706 stars spanning a wide range in atmospheric parameters. We have defined a new set of near-IR indices, CaT*, CaT and PaT, which mostly overcome the limitations of previous definitions, the former being specially suited for the measurement of the Caii triplet strength corrected for the contamination from Paschen lines. We also present a comparative study of the new and the previous Ca indices, as well as the corresponding transformations between the different systems. A thorough analysis of the sources of index errors and the procedure to calculate them is given. Finally, index and error measurements for the whole stellar library are provided together with the final spectra.