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Unconventional superconductivity, in particular, in noncentrosymmetric systems, has been a long-sought topic in condensed matter physics. Recently, Re-based superconductors have attracted great attention owing to the potential time-reversal symmetry breaking in their superconducting states. We report the superconducting properties of noncentrosymmetric compounds TaxRe1 – x with 0.1 ≤ x ≤ 0.25, and find that the superconducting transition temperature reaches a maximum of ∼8 K at the optimal level x = 0.15. Nevertheless, muon-spin rotation and relaxation measurements reveal no time-reversal symmetry breaking existing in its superconducting state, which is in sharp contrast to both centrosymmetric Re metal and many other noncentrosymmetric Re-based superconductors. [ABSTRACT FROM AUTHOR]