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Design floods allow the hydrological sizing of hydraulic works. When hydrometric data is not available, design floods are estimated using hydrological methods that are based on design rains. The most common records used to estimate design rains are the annual maximum daily precipitations (PMD), this, due to the scarcity of rainfall recorder stations. The impacts of climate change and/or the alteration of the geographic environment of rain-gauge stations cause PMD records to show trends and therefore these records become non-stationary. In order to estimate predictions of low probability of exceedance a probabilistic analysis of the non-stationary PMD records can be performed. A simple approach without computational difficulties is based on the extension of the method of L moments applied to the general distribution of extreme values (GVE) with its location parameter (u) variable with time (t) in years, which is entered as a covariate. When the trend in the PMD register is linear, the probabilistic model GVE(1) is applied in which u(t) = mu(0) + mu(1).t and when the trend is curve the model GVE(2) with ut = mu(0) + mu(1).t + mu(2).t(2) is used. Thus, the GVE(1) distribution has four fit parameters (mu(0), mu(1), a, k) and five for the GVE(2) distribution (mu(0), mu(1), mu(2), a, k). Four numerical applications are described and the analysis of their results shows the simplicity of the extension of the L moments method and its versatility to estimate predictions within the historical record and to the future.