This study presents a new method based on short time Fourier analysis giving a local unbiased estimation of the attenuation in biological tissue. Short time Fourier analysis concepts are well adapted to process time echographic signals which are non stationary. The interest of Short Time Fourier Analysis is to give an estimation of the signal spectral composition as a function of time. It will be shown that the time dependence of the spectral centre of gravity allows to deduce easily the frequency dependant attenuation. The near field low pass filtering effect due to diffraction is emphasized. A numerical calibration technique developed for each transducer which corrects these effects is described.Experimental results obtained from tissue like phantom and from in vivo liver tissue are presented.