In recent years, palmprint recognition has gained increased interest and has been a focus of significant research as a trustworthy personal identification method. The performance of any palmprint recognition system mainly depends on the effectiveness of the utilized feature extraction approach. In this paper, we propose a three-step approach to address the challenging problem of contactless palmprint recognition: (1) a pre-processing, based on median filtering and contrast limited adaptive histogram equalization (CLAHE), is used to remove potential noise and equalize the images’ lighting; (2) a multiresolution analysis is applied to extract binarized statistical image features (BSIF) at several discrete wavelet transform (DWT) resolutions; (3) a classification stage is performed to categorize the extracted features into the corresponding class using a K-nearest neighbors (K-NN)-based classifier. The feature extraction strategy is the main contribution of this work; we used the multiresolution analysis to extract the pertinent information from several image resolutions as an alternative to the classical method based on multi-patch decomposition. The proposed approach was thoroughly assessed using two contactless palmprint databases: the Indian Institute of Technology—Delhi (IITD) and the Chinese Academy of Sciences Institute of Automatisation (CASIA). The results are impressive compared to the current state-of-the-art methods: the Rank-1 recognition rates are 98.77% and 98.10% for the IITD and CASIA databases, respectively.