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Adverb: inexcusably  ,i-nik'skyoo-zu-blee or ,i,nek'skyoo-zu-blee
  1. In an unpardonable manner or to an unpardonable degree
    "he was inexcusably cruel to his wife";
    - unpardonably, unforgivably
  2. Without any excuse
    "he is inexcusably harsh on her";
    - unjustifiably

Antonym: justifiably, pardonably