The Landsat Multispectral Scanner (MSS) data sensed by the Landsat 1–5 satellites make up a significant portion of the early Landsat data record. However, accurate MSS image geolocation has been difficult to achieve systematically due to a number of factors associated primarily with the older sensor and satellite technology. As of August 2019, only 49% of the Landsat MSS archive could be processed at the highest-level L1TP (precision and terrain corrected) level, and the remainder were processed as L1GS (systematically corrected) with inaccurate geolocation and no terrain correction. This paper presents a methodology to improve the geolocation of MSS time series. The methodology uses an area- and feature-based least-squares matching scale-space algorithm, with a time series registration implementation, that we developed previously using Landsat-8 and Sentinel-2 imagery. The methodology requires that at least three L1TP images in the time series acquired over a given path/row are available. A linear combination of a polynomial transformation and multiple radially symmetric radial-basis-functions (RBFs) to model local uncorrected terrain relief effects present in the L1GS images are used. The processing is automated and applied in two passes. The first pass screens L1TP images to select the well-aligned ones that are used as references. The second pass registers the target images, including the L1GS images and any misaligned L1TP images, to all the reference L1TP images. The transformation coefficients for each registered target image are derived by least-squares adjustment using densely-matched tie-points between the target and the reference images. The methodology is demonstrated using 12 months of Landsat-4 MSS images at four Landsat path/row locations that contain agricultural, mountainous, and coastal regions, including a total of 43 L1TP and 31 L1GS images. There were sufficient tie-points to characterize the degree of misregistration of 14 L1GS images that had significant mean misregistration shifts ranging from 7.33 to 17.42 60 m pixels. In addition, at one site, two L1TP images were found to be misaligned and have mean misregistration shifts of 1.27 and 2.20 60 m pixels. The methodology provides sub-pixel registration accuracy - after registration, the mean misregistration shifts for the 14 L1GS and two misaligned L1TP images varied from only 0.10 to 0.41 60 m pixels. The methodology does not use a digital elevation model, and examples illustrate that although the RBF transformations can compensate terrain relief distortion effects, larger (~0.5 to 1.0 pixel) misregistration errors can remain in areas with highly variable terrain relief. Results are also provided for Landsat-1 MSS imagery to demonstrate the applicability of the methodology to even the earliest part of the Landsat record. Detailed qualitative and quantitative results are presented and indicate the potential of the methodology to improve the geolocation of the Landsat MSS data record that is discussed with recommendations for future research.