We investigate how relativity influences the spin correlation of entangled fermions described by wave packets and measured by moving detectors. In particular, we show that the Clauser-Horne-Shimony-Holt (CHSH) Bell inequality is not violated by quantum mechanics when the left and right spin detectors move fast enough. We also show that the violation of the Bell-CHSH inequality measured by the moving detectors decreases with increasing width of the initial wave packet.Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)