We present the results of a novel Mossbauer experiment in a rotating system, implemented recently in Istanbul University, which yields the coefficient k=0.69+/-0.02 within the frame of the expression for the relative energy shift between emission and absorption lines dE/E=ku2/c2. This result turned out to be in a quantitative agreement with an experiment achieved earlier on the subject matter (A.L. Kholmetskii et al. 2009 Phys. Scr. 79 065007), and once again strongly pointed to the inequality k>0.5, revealed originally in (A.L. Kholmetskii et al. 2008 Phys. Scr. 77, 035302 (2008)) via the re-analysis of Kundig experiment (W. Kundig. Phys. Rev. 129, 2371 (1963)). A possible explanation of the deviation of the coefficient k from the relativistic prediction k=0.5 is discussed.