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Firstly, a new refinement of the Heinz inequality is given. Then, by using the inequality, some new refinements of Heinz inequalities of matrices are given. Lastly, we declare that the results are better than the ones in (Kittaneh in Integral Equ. Oper. Theory 68:519-527, 2010), but we cannot say that our results are better than the ones in (Feng indoi:10.1186/1029-242x-2013-424 fatcat:4e6okgyvejgyhe2ezw3iqkkgke