Recently, climate change makes itself felt at increasing levels due to rising temperatures, irregular precipitation patterns and changing weather events. Although the frequently used Mann-Kendall (MK) method has disadvantages such as needing serial independence, it helps to detect monotonic trends to investigate climate change effects on a given time series. Climate change may have different features on different levels such as the lows and highs of a given time series, leading to non-monotonic trends. Innovative trend analysis (ITA) as an innovative trend analysis method detects non-monotonic trends, which MK cannot. In this study, MK method is improved to detect non-monotonic trends (non-monotonic MK) and applied for Murat River basin, a branch of Euphrates River, precipitation series at Bingöl, Muş, and Ağrı meteorological stations. Although classical MK method cannot detect any trend on the river basin, non-monotonic MK (NMK) method detects two important decreasing (increasing) trends on the low (high) values of Bingöl and Muş (Bingöl) stations. Also, stationarity analysis is applied through the statistical significance level concept for the river basin precipitation series using the NMK method. Bingöl station has a non-stationary precipitation series with a value of 3.07 and 95% confidence level, while Muş station has a remarkable value of 1.58, Ağrı station conserves its stationarity characteristic on the precipitation series. It is hoped that the newly developed NMK method will help to understand the effects of climate change on hydro-meteorological historical records and predict future events for more efficient hydraulic structure designs.