By analyzing the available data on strange hadrons in central Pb+Pb collisions from the NA49 Collaboration at the Super Proton Synchrotron (SPS) and in central Au+Au collisions from the STAR Collaboration at the Relativistic Heavy-Ion Collider (RHIC) in a wide collision energy range from √ sNN = 6.3 GeV to 200 GeV, we find a possible non-monotonic behavior in the ratioof K + , Ξ − , φ, and Λ yields as a function of √ sNN. Based on the quark coalescence model, which can take into account the effect of quark density fluctuations on hadron production, a possible non-monotonic behavior in the dependence of the strange quark density fluctuation on √ sNN is obtained. This is in contrast to the coalescence model that does not include quark density fluctuations and also to the statistical hadronization model as both fail to describe even qualitatively the collision energy dependence of the ratio O K-Ξ-φ-Λ . Our findings thus suggest that the signal and location of a possible critical endpoint in the QCD phase diagram, which is expected to result in large quark density fluctuations, can be found in the on-going Bean Energy Scan program at RHIC. PACS numbers: 25.75.-q, 25.75.DwThe main goal of the experiments on heavy-ion collisions at relativistic energies is to study the properties of strongly interacting matter under extreme conditions, especially those of the quark-gluon plasma (QGP), the hadronic matter, and the transition between these two phases of matter [1][2][3]. Studies based on lattice quantum chromodynamics (LQCD) calculations [4] and various effective models [5][6][7] have indicated that the transition between the QGP and the hadronic matter is a smooth crossover at vanishing baryon chemical potential (µ B ) but likely changes to a first-order phase transition at large µ B , with an associated critical endpoint (CEP) or a tricritical endpoint seperating these two transitions [8].Locating the position of the CEP in the QCD phase diagram is one of the most important issues in particle and nuclear physics. To search for this CEP, experiments have been carried out already at the Beam Energy Scan programs at SPS [9-12] and at RHIC [13,14] as well as planned at the future Facility for Antiproton and Ion Research (FAIR) and Nuclotron-based Ion Collider Facility (NICA).As suggested in Ref.[15], the QCD phase transition can be probed by studying the fluctuations of physical observables in relativistic heavy ion collisions. This is because enhanced long-wavelength fluctuations near the CEP can lead to singularities in all thermodynamic observables. In heavy-ion collisions, these fluctuations have been studied by using experimental data on an event-by-event basis and looking at event-by-event fluctuations [16,17]. For example, the fourth-order fluctuation of net-proton distribution had been measured in the BES program by the STAR Collaboration, and a possible non-monotonic behavior in its dependence on the center-of-mass collision energy √ s NN was observed [18].Also, large baryon density fluctuations are expected to be...