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In this paper, we propose a new method to obtain C¹ MPH quartic Hermite interpolants generically for any C¹ Hermite data, by using the speed raparametrization method introduced in [16]. We show that, by this method, without extraordinary processes (C½ Hermite interpolation introduced in [13]) for non-admissible cases, we are always able to find C¹Hermite interpolants for any C¹ Hermite data generically, whether it is admissible or not.