An-in-pile experimental technique to measure the decay constants and the relative abundances of the delayed neutron groups applicable for a given reactor system is presented. The method is based on a least-squares-fitting technique that simultaneously fits a series of transients produced by small reactivity perturbations to a reactor operating initially at delayed critical. The function that is least-squares fit is the analytic solution (written in terms of an arbitrary number of delayed neutron groups) as obtained by the point reactor model for the reactor response following a step change in reactivity. The application of the method does not require any knowledge of the size of the reactivity perturbations, and the method is independent of the detector efficiency. The results are based solely on the measurable quantities of relative power, time, and one measurable root of the Inhour equation.