Crystals of Yb3+ doped Rb2MnCl4 exhibit very intense yellow-orange Mn2+ T-4(1g) --> (6)A(1g) upconversion luminescence under near-infrared F-2(7/2) --> F-2(5/2) Yb3+ excitation around 1 mum at 15 K. Excitation with 10 ns pulses indicates that the upconversion process consists of a sequence of ground-state and excited-state absorption steps. The upconversion mechanism is cooperative, involving both Yb3+ and Mn2+ ions in the crystal, and we postulate an exchange mechanism between adjacent Yb3+ and Mn2+ ions to account for the unusually high efficiency of the process. The efficiency of the upconversion process is dependent on the nature of the Yb3+-Mn2+ connectivity. The upconversion in Rb2MnCl4:Yb3+, with a linear Yb3+-Cl--Mn2+ arrangement, is 3 orders of magnitude more efficient than in the Yb3+-(Br-)(3)-Mn2+ arrangement of face-sharing octahedra in CsMnBr3:Yb3+.