Since the introduction of turbo codes in 1993, many new applications for this family of codes have been proposed. One of the latest, in the context of digital fingerprinting, is called turbo fingerprinting codes and was proposed by Zhang et al.. The main idea is a new fingerprinting code composed of an outer turbo code and an inner code based on the Boneh-Shaw model. The major contribution of this paper is a new analysis of this new family of codes that shows its drawbacks. These drawbacks must be considered in order to perform a correct design of a turbo fingerprinting scheme otherwise the scheme cannot retrieve the traitor users which is the main goal of digital fingerprinting scheme. Moreover, the identification of these drawbacks allows to discuss an entirely new construction of fingerprinting codes based on turbo codes.