Abstract We report the result of the Co59 nuclear spin-lattice relaxation time T1 measurements in the diamagnetic monoboride CoB. The analysis of the data, in the 4.2–300 K temperature range, allows us to separate three contributions to the relaxation rate: first a Korringa process, (T1KT)−1= 0.21 sec−1K−1 (in good agreement with the temperature independent isotropic Knight shift) from which we deduced the Co59 hyperfine constant A=6.2 ×10−6eV, second an impurity contribution independent of temperature and third a quadrupolar term, T −1 1Q =3560 ( T θ D ) 2 E( T θ D ) sec −1 , which is predominant at high temperature and well explained by the Van Kranendonk theory. It seems that it was the first time that such a quadrupolar effect was detected in a metallic compound. A remarkable coherency between Lundquist's three bands model and our experimental results has to be noted.