Under the conditions of system linearity and stationarity of the precipitation process we derive the hyetograph associated with any given flood discharge Q, using best linear unbiased estimation (BLUE) theory. The BLUE hyetograph depends explicitly on the correlation characteristics of the rainfall process and the instantaneous unit hydrograph (IUH) of the basin. When the correlation time of the rainfall process is short relative to the dispersion of the IUH, the shape of the BLUE hyetograph is the mirror image of the IUH itself. In the opposite case the design hyetograph is the mirror image of the rainfall correlation function. The procedure is extended from lumped to semidistributed and distributed basins. In the latter case we obtain simultaneous design hyetographs for each subbasin or each site in the basin. The analytical findings and the possibility of regionalization are verified using synthetic and recorded rainfall time series, with excellent agreement in both cases. Because of its simplicity, robustness, and theoretical basis the proposed procedure should be appealing for practical use, particularly when not only the peak but the entire flood hydrograph is required. ¿ 1999 American Geophysical Union