Produced partons have large local relative orbital angular momentum along the direction opposite to the reaction plane in the early stage of non-central heavy-ion collisions. Parton scattering is shown to polarize quarks along the same direction due to spin-orbital coupling. Such global quark polarization will lead to many observable consequences, such as left-right asymmetry of hadron spectra, global transverse polarization of thermal photons, dileptons and hadrons. Hadrons from the decay of polarized resonances will have azimuthal asymmetry similar to the elliptic flow. Global hyperon polarization is studied within different hadronization scenarios and can be easily tested.PACS numbers: 13.88.+e, 12.38.Mh, 25.75.Nq Strong transverse polarization of hyperons has been observed in unpolarized p + p and p + A collisions since the 1970's [1]. Given the beam and hyperon momenta p and p H , hyperons produced in the beam fragmentation region are found transversely polarized in the direction perpendicular to the hyperon production plane,Polarizations of Λ, Ξ andΞ are negative while Σ andΣ's are positive. In the meantime,Λ and Ω are not transversely polarized. Although the origin for such striking transverse hyperon polarization is still in debate, one can relate it to the single-spin left-right asymmetries observed in hadron-hadron collisions with transversely polarized beam [2], which in turn can be attributed to the orbital angular momenta (o.a.m.) of the valence quarks in a polarized nucleon [3,4,5], or fragmentation functions of transverse polarized quarks [6] as well as twist-3 parton correlations in nucleons [7]. It has also been suggested [8,9] that hyperon polarization could disappear due to the formation of QGP.In this Letter, we show that parton interaction in noncentral heavy-ion collisions leads to a global quark polarization along the opposite direction of the reaction plane,as determined by the nuclear impact parameter b. This global polarization is essentially a local manifestation of the global angular momentum of the colliding system through interaction of spin-orbital coupling in QCD. It will have far reaching consequences in non-central heavyion collisions, such as left-right asymmetry of hadron spectra in the reaction plane, global transverse polarization of direct photons, dileptons and hadrons with spin. Within different hadronization scenarios, we will discuss hyperon polarization as a result of the global quark polarization. Possible contribution from final state hadronic interaction will also be discussed. Let us consider two colliding nuclei with the beam projectile moving in the direction of the z axis, as illustrated in Fig. 1. We define the impact parameter b (alongx) as the transverse distance of the projectile from the target nucleus and the reaction plane as given by n b (alongŷ) in Eq. (1). Partons produced in the overlapped region of the collision will carry a global angular momentum along the direction opposite to the reaction plane (−ŷ). A thermalized QGP requires final state par...