We present the results of a novel Mossbauer experiment in a rotating system, implemented recently at 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 Delta E/E = ku(2)/c(2). This result turned out to be in quantitative agreement with an experiment achieved earlier on the subject matter (Kholmetskii et al. Phys. Scr. 79, 065007 (2009)), and once again strongly pointed to the inequality k > 0.5, revealed originally in (Kholmetskii et al. Phys. Scr. 77, 035302 (2008)) via the re-analysis of Kundig's experiment (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.