By confining water in nanopores, so narrow that the liquid cannot freeze, it is possible to explore its properties well below its homogeneous nucleation temperature T(H) approximately equals 235 K. In particular, the dynamical parameters of water can be measured down to 180 K, approaching the suggested glass transition temperature T(g) approximately equals 165 K. Here we present experimental evidence, obtained from Nuclear Magnetic Resonance and Quasi-Elastic Neutron Scattering spectroscopies, of a well defined decoupling of transport properties (the self-diffusion coefficient and the average translational relaxation time), which implies the breakdown of the Stokes-Einstein relation. We further show that such a non-monotonic decoupling reflects the characteristics of the recently observed dynamic crossover, at approximately 225 K, between the two dynamical behaviors known as fragile and strong, which is a consequence of a change in the hydrogen bond structure of liquid water.