The antiferromagnetic Blume-Emery-Griffiths model in an external magnetic field is studied by using the exact recursion relations on the Bethe lattice for arbitrary values of biquadratic and for negative values of bilinear interactions. We have studied the thermal variations of two-sublattice magnetizations belonging to spin-1 BEG model to obtain the phase diagrams on the (H/vertical bar J vertical bar,kT/vertical bar J vertical bar) plane. As a result, we have found that the system presents second- and first-order phase transitions, therefore, tricritical points for appropriate values of K/vertical bar J vertical bar, D/vertical bar J vertical bar and q. We have also found that the second-order phase transition lines exhibit reentrant phenomena in temperature, besides it also shows reentrant phenomena for the first-order phase lines in external magnetic field for q=4 and 6. (C) 2005 Elsevier B.V. All rights reserved.