A sequence of functions (curves) collected over time is called a functional time series. The abundance of such observations has made functional time series analysis one of the popular branches of research in statistics. The main goal of functional time series analysis is to predict and quantitatively describe the stochastic mechanisms that have led to the production of functions. In this regard, it is necessary to decompose the functional time series into trend, time period, and error components. However, before decomposition, we need to identify and detect such components. Therefore, in this paper, a nonparametric method for examining and detecting the presence of a trend in a functional time series using record functions is introduced. Then, by implementing and using this method in a functional time series, its application is investigated. Finally, the efficiency of this method for detecting trends in a set of real fertility rate data is investigated.