The polarization of quarkonium states produced in hadron collisions exhibits strong non-perturbative effects -for example, at small transverse momentum pt charmonia appear unpolarized, in sharp contradiction to the predictions of perturbation theory. The quark-gluon plasma is expected to screen away the non-perturbative physics; therefore those quarkonia which escape from the plasma should possess polarization as predicted by perturbative QCD. We estimate the expected J/ψ polarization at small pt, and find that it translates into the asymmetry of the e + e − (µThe possibility to form quark-gluon plasma in heavy ion collisions is an intriguing problem of strong interaction physics. To establish the formation of plasma, a number of signatures were proposed; here we will concentrate on heavy quarkonia. Suppression of heavy quarkonium states has been suggested long time ago by Matsui and Satz [1] as a signature of the deconfinement phase transition in heavy ion collisions. Their, by now wellknown, idea is that the Debye screening of the gluon exchanges will make the binding of heavy quarks into the bound states impossible or unlikely once a sufficiently high temperature is reached. The lack of quarkonium states would thus signal deconfinement; this effect was indeed observed and studied in detail at CERN SPS by the NA38 [2] and NA50 Collaborations [3]. The results on J/ψ production at RHIC have recently been presented by the PHENIX Collaboration [4]. The observations of quarkonium suppression have been interpreted as a signal of quark-gluon plasma formation [5]. However, different conclusions were reached in [6], where it was argued that the effect may arise due to quarkonium collisions with the comoving hadrons. Additional tests of the quark-gluon plasma formation could help to clarify the situation.In this note we propose to use for the diagnostics of the quark-gluon plasma those heavy quarkonia which escape from it. This would require experimental measurements of quarkonium polarization, which can be reconstructed from the angular distributions of quarkonium decaysdileptons and/or photons. For J/ψ states, one would need to measure the angular distribution of electrons (or muons) in the J/ψ → e + e − decay in J/ψ rest frame relative to the direction of its momentum. (We will concentrate on J/ψ's at relatively small p t , which dominate the total production cross section.)Let us first formulate what we mean by the quarkgluon plasma, since different definitions sometimes may result in misunderstanding. We define the quark-gluon plasma as a gas of quarks and gluons in which the interactions can be described by perturbative QCD and non-perturbative effects are either absent or can be neglected. We will not need to specify the properties of this state of matter in more detail to develop our idea; let us now turn to the dynamics of quarkonium production.It is well-known that the description of the data on heavy quarkonium production within the framework of perturbative QCD (pQCD) meets with siginificant difficulties. Bo...