This paper describes a method for the determination of rare earths at ppb level by coprecipitative preconcentration using iron (III) hydroxide as collector. The precipitates are collected by vacuum filtration onto filter paper containing ethyl cellulose powder. After drying the residue was powdered and pressed into pellets for quantitation by energy dispersive x-ray fluorescence (EDXRF) via their characteristic K-x ray lines. Various parameters that influence coprecipitative preconcentration of rare earths on iron (III) hydroxide were optimized. Further, a numerical method based on simple least square procedure was developed for smoothing and differentiation of the EDXRF data which had been digitized and averaged. By carrying out the least square calculations on a computer via convolution of the EDXRF data (obtained after co-precipitative preconcentration) with properly chosen integers facilitates the determination of as low as 10 ppb each of rare earths. © 1989, Taylor & Francis Group, LLC. All rights reserved.