Diffusion MRI has become one of the most powerful tools for the detection of acute stroke. The signal attenuation caused by the diffusion process is normally assumed to be exponential. The decay constant which is often called the “apparent diffusion coefficient” (ADC) is measured by 2 or 3 points in clinical applications yielding mono‐exponential decay curves. The diffusion signal attenuation of water molecules on human brain was measured with a certain pulse sequence. The sequence was modified to work over a range of diffusion times and high gradients. The decay was measured precisely for 96 b‐values up to the maximum possible gradient amplitude of 28.8 mT/m. A significant deviation from mono‐exponential behavior was observed consistent to the multi‐exponential model. The NNLS‐diff computational code, using a non‐negative least squares (NNLS) algorithm was developed for the data analysis. The diffusion time dependence of human brain tissue was studied for diffusion times between 20 to 53 ms using 16 b‐values ranged from b=0 to the maximum possible b‐value in each case. At all diffusion times there was a diffusion coefficient at approximately 1×10−3 mm2/s and another at about 7×10−5 mm2/s. For some diffusion times a small contribution at about 1×10−2 mm2/s was also detected. Our results were consistent with work of others. However, we observe a small diffusion time dependence for the smallest diffusion coefficient which has not previously been reported. More work is required to identify the source of the new observation.