Different statistical methodologies can be employed to identify possible trend components in any hydro-meteorological time series. A pre-whitening (P-W) procedure has been suggested to reduce the serial correlation effect on Mann-Kendall (M-K) trend analysis. In this paper, instead of P-W, an over-whitening (O-W) procedure is suggested, which generates serially independent series with the same trend slope value. Analytically necessary formulations for O-W are presented with a non-parametric but simple innovative trend assessment procedure, which are supported by extensive simulation studies. The applications of the methodology are presented for eight factual time series records from tropical, temperate and arid regions including temperature, rainfall, streamflow, relative humidity and CO2 concentrations for different short and long durations. Relative humidity and CO2 records are monthly time series and, hence, there are trend and periodicity components. It is noticed in all cases that the natural trends remain as they were after the O-W procedure, thus providing an opportunity to determine reliably the trends embedded even in the serially dependent series. The O-W procedure is applicable even in the cases of periodicity in the original records.