In this paper, a new global time series averaging method is proposed for improving k-means clustering performance for observed signals or time series data. The proposed method is different from most commonly used time series averaging methods, such as pairwise averaging method (PA), nonlinear alignment and averaging filter (NLAAF), prioritized shape averaging (PSA) and dynamic time warping (DTW) barycentre averaging (DBA). The implementation mechanism of the new method is as follows: i) Choose an initial cluster centre sequence based on the within-cluster distance; ii) Compute the weight values and extract the optimal matching path according to the dynamic time warping distance between the centre sequence and all the rest sequences, and iii) Calculate the average sequence using the rest sequences, the optimal matching paths and the weight values. To demonstrate the performance of the proposed method, the aforementioned four existing averaging methods, along with the proposed method, are applied to a benchmark time series dataset containing 600 sequences. The experimental results show that the proposed method outperforms all the four compared methods, in terms of the sum of within-cluster distance and adjusted Rand index.