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The oncoming climate changes will cause impact on the ecosystems, on all branches of the international economy, on the human health and quality of life. The importance of assessing trends in climate extremes is often emphasized. As far as this trend could be quantified by means of various statistical techniques, the final outcome can differ from method to method. Main aim of the present study is to demonstrate the impact of the choice, which more of less is a matter of arbitrariness, for estimation of the slope of the linear trend. The two most widely applied regression methods in the climatology are considered: the ordinary least squares and the Theil-Sen estimator. Objects of the linear trend analysis are 67-years long series of selected ETCCDI climate indices on annual basis, part of the database ClimData. The main conclusion is that both regression methods produce different, in the common case nonnegligible results concerning the slope of the line, e.g. trend estimation. This fact is strengthened by presence of even few "strange" data points in the analyzed time series.