Finding an overall linear trend is a common method in scientific studies. It is almost a requirement when one intends to study variability. Nevertheless, when dealing with long climate temporal series, fitting a straight line only seldom has a relevant meaning. This paper proposes and describes a new methodology for finding overall trends, and, simultaneously, for computing a new set of climate parameters: the breakpoints between periods with significantly different trends. The proposed methodology uses a least-squares approach to compute the best continuous set of straight lines that fit a given time series, subject to a number of constraints on the minimum distance between breakpoints and on the minimum trend change at each breakpoint. The method is tested with three climate time series.