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We consider the problem of scheduling jobs on related machines owned by selfish agents. Previously, Archer and Tardos showed a 2-approximation randomized mechanism which is truthful in expectation only (a weaker notion of truthfulness). We provide a 5-approximation deterministic truthful mechanism, the first deterministic truthful result for the problem. In case the number of machines is constant, we provide a deterministic Fully Polynomial Time Approximation Scheme (FPTAS) algorithm, and a suitable payment scheme that yields a truthful mechanism for the problem. This result, which is based on converting FPTAS to monotone FPTAS, improves a previous result of Auletta et al, who showed a (4+ε)-approximation truthful mechanism.