Climatic teleconnections are often used to interpret and sometimes to predict precipitation temporal variability at various time scales. However, the teleconnections are intertwined between the effects of multiple large-scale climate signals which are often interdependent. Each climate signal is composed of multitemporal components, which may result in different teleconnection patterns. The time lags of precipitation response may vary with climate signals and their multitemporal components. In order to effectively address these problems, a multiresolution analysis (MRA) with a discrete wavelet transform is utilized, and a stepwise linear regression model based on MRA and cross correlation analysis is developed in this study. The method is applied to examine monthly precipitation teleconnections in South Australia (SA) with five large-scale climate signals. The MRA first decomposes each of original monthly precipitation anomaly and climate signals into several component series at different temporal scales. Then the hierarchical lag relationships between them are determined for regression modeling using cross-correlation analysis. The results indicate that the MRA-based method is able to reveal at which time scale(s) and with what time lag(s) the teleconnections occur, and their spatial patterns. The method is also useful to examine the time-scale patterns of the interdependence between climate signals. These altogether make the MRA-based method a promising tool to address the difficulties in the climate teleconnection studies. The multiple linear regression based on MRA-decomposed climate signals is expected to better interpret monthly precipitation temporal variability than that based on the original climate signals.