We prove the existence of a flaw which we individuated in the design of the Object-Independent Authorization Protocol (OIAP), which represents one of the building blocks of the Trusted Platform Module (TPM), the core of the Trusted Computing Platforms (TPs) as devised by the Trusted Computing Group (TCG) standards. In particular, we prove, also with the support of a model checker, that the protocol is exposed to replay attacks, which could be used for compromising the correct behavior of a TP. We also propose a countermeasure to undertake in order to avoid such an attack as well as any replay attacks to the aforementioned protocol.