Although a great number of single-ion magnets (SIMs) and spin-crossover (SCO) compounds have been discovered, multifunctional materials with the combination of SCO and SIM properties are extremely scarce. Here magnetic studies have been carried out for a mononuclear, five-coordinate cobalt(ii) complex [Co(3,4-lut)4Br]Br (1) with square pyramidal geometry. Direct-current magnetic measurement confirms the spin transition between the S = 1/2 and 3/2 states in the range of 150-290 K with a small hysteresis loop. Frequency- and temperature-dependent alternating-current magnetic susceptibility reveals slow magnetization relaxation under an applied dc field of 3000 Oe. The work here presents the first instance of the five-coordinate mononuclear cobalt(ii)-based SIM exhibiting the thermally induced complete SCO.