We present the first measurement on Nernst effect in the normal state of odd-parity, spin-triplet superconductor Sr$_{2}$RuO$_{4}$. Below 100 K, the Nernst signal was found to be negative, large, and, as a function of magnetic field, nonlinear. Its magnitude increases with the decreasing temperature until reaching a maximum around $T^*$ $approx$ 20 - 25 K, below which it starts to decrease linearly as a function of temperature. The large value of the Nernst signal appears to be related to the multiband nature of the normal state and the nonlinearity to band-dependent magnetic fluctuation in Sr$_{2}$RuO$_{4}$. We argue that the sharp decrease in Nernst signal below $T^*$ is due to the suppression of quasiparticle scattering and the emergence of band-dependent coherence in the normal state. The observation of a sharp kink in the temperature dependent thermopower around $T^*$ and a sharp drop of Hall angle at low temperatures provide additional support to this picture.
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