The use of an amplitude/phase retrieval algorithm in electrical bioimpedance spectroscopy (EIS) that allows a new technique to reconstruct the impedance spectrum in the frequency-domain is reported. To the authors' knowledge this is the first time the proposed algorithm has been used to calculate the modulus or phase of a bioimpedance in EIS from one of these two experimentally obtained parameters. The algorithmic technique is demonstrated in EIS, when wide-bandwidth amplifiers,phase-detectors, and high speed converters determine spectra over frequencies up to 500 kHz at isolated points in the frequency interval. Simulated data from bioimpedance models (Cole and 2R1C circuit impedance functions) and experimental data from a known electrical impedance are used to show the applicability and limitations of the technique with a phase retrieval and a modulus retrieval algorithm.Results comparing this technique with the Kramers-Kronig technique that retrieves the imaginary part of an impedance from its real part are also discussed.