A new non-linear limb-darkening law, based on the Least-Squares Method (LSM), is presented. This law is able to describe the intensity distribution much more accurately than any of the old ones given that the differences I(model)-I(fitting) are of some order of magnitude smaller than those derived from other approximations. This new law shows several advantages: it represents well the intensity distribution, the flux is conserved with high accuracy and it permits the use of a single law for the whole HR Diagram since that the bi-parametric laws are only marginally valid in certain range of effective temperatures. The limb-darkening coefficients are computed for the 12 commonly used photometric bands u v b y U B V R I J H K. Bolometric and monochromatic calculations are also available. The computations are presented for 19 metallicities ranging from 10^-5^ up to 10^+1^ solar abundances, with log(g) varying between 0 and 5.0 and effective temperatures between 2000K-50000K. Results for microturbulent velocities of 0, 1, 2, 4, 8 km/s are also available. With this set of data it was possible to investigate, for the first time, the influence of such parameters in the limb-darkening. Limb-brightening, instead of limb-darkening, was detected for some models. It is shown that the limb-darkening coefficients derived using the Flux Conservation Method (FCM) do not describe very well the intensity distribution, mainly near the border of the disk. On the contrary, the present coefficients, based on the LSM, represent very well the function I({mu}) at any part of the disk for any filter or wavelength, log(g), effective temperature, metallicity and microturbulent velocity. The results are presented here as synthetic tables containing the limb-darkening coefficients. The 46 tables announced in the paper are also accessible as the "original.tar" file.