Multitemporal cross-sensor imagery is fundamental for the monitoring of the Earth’s surface over time. However, these data often lack visual consistency because of variations in the atmospheric and surface conditions, making it challenging to compare and analyze images. Various image-normalization methods have been proposed to address this issue, such as histogram matching and linear regression using iteratively reweighted multivariate alteration detection (IR-MAD). However, these methods have limitations in their ability to maintain important features and their requirement of reference images, which may not be available or may not adequately represent the target images. To overcome these limitations, a relaxation-based algorithm for satellite-image normalization is proposed. The algorithm iteratively adjusts the radiometric values of images by updating the normalization parameters (slope (α) and intercept (β)) until a desired level of consistency is reached. This method was tested on multitemporal cross-sensor-image datasets and showed significant improvements in radiometric consistency compared to other methods. The proposed relaxation algorithm outperformed IR-MAD and the original images in reducing radiometric inconsistencies, maintaining important features, and improving the accuracy (MAE = 2.3; RMSE = 2.8) and consistency of the surface-reflectance values (R2= 87.56%; Euclidean distance = 2.11; spectral angle mapper = 12.60).