In this article, an existing exact algorithm for identifying a continuous transfer function from frequency data, giving major importance to phase data, is further developed. The new version allows identifying a digital transfer function, or a continuous fractional order transfer function with a fixed order of commensurability (i.e. a ratio of two polynomials in s(alpha), alpha is not an element of Z). This is straightforward if the desired transfer function is to have only zeros or only poles; if a transfer function with both zeros and poles is sought, however, a numerical method must be resorted to.