By use of Ge-detectors of the OSIRIS-collaboration [1] in connection with the 12 detector IPAC apparatus of our laboratory [2] a precise measurement of the g-factor of the 4~ rotational state of 16~ was performed. The directional correlations of the three 7-7 cascades, 1003-197 keV, 1103-197 keV and 1115-197 keV, which are weakly populated in the decay of 72.3 d t6~ were observed simultaneously. The integral rotations in the static hyperfine field of DyTb at 4.2 K were measured. The g-factor g(4[) = + 0.350 (20) was derived. By comparison with the magnetic splitting of the 2~ rotational state observed in the same environment by a M6ssbauer experiment [3] the ratio of the two g-factors was derived as g(4~)/g(2 +) = + 0.91(5).For the high energy lines we derived from the measured directional correlations the El~M2 mixing parameters: c~(1003 keV) = + 0.005(4); 6(1103 keV) = -0.020(22), and c5(1115 keY) = + 0.010 (4)