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I don't really mean "deleting" them, but aren't these badly named? I don't think you can say "with mute h" in English, doesn't it have to be "with a mute h". Mglovesfun (talk) 21:09, 1 September 2009 (UTC)
1997, Annie Heminway et al., 1001 Pitfalls in French Third edition, Barron's educational series, page 131: 
A further difficulty for the French as well as us is that with mute h an "elision" and "liaison" are required[...]
2003, Glanville Price, A comprehensive French grammar, Blackwell publishing, page 3: 
Words (most of them of Latin or Greek origin) beginning with mute h function as if it were not there, i.e. as if they began with a vowel.
2009, A.P. Huguenet, Hossfeld's New Practical Method for Learning the French Language, BiblioLife, page 136: