Topochemical reduction of the ordered double perovskite LaSrNiRuO6 with CaH2 yields LaSrNiRuO4, an extended oxide phase containing infinite sheets of apex-linked, square-planar Ni(1+)O4 and Ru(2+)O4 units ordered in a checkerboard arrangement. At room temperature the localized Ni(1+) (d(9), S = (1)/2) and Ru(2+) (d(6), S = 1) centers behave paramagnetically. However, on cooling below 250 K the system undergoes a cooperative phase transition in which the nickel spins align ferromagnetically, while the ruthenium cations appear to undergo a change in spin configuration to a diamagnetic spin state. Features of the low-temperature crystal structure suggest a symmetry lowering Jahn-Teller distortion could be responsible for the observed diamagnetism of the ruthenium centers.