Summary: In this paper, we make some considerations about admissible orders on the set of closed subintervals of the unit interval \(\mathbb{I} [0, 1]\), i.e. linear orders that refine the product order on intervals. We propose a new way to generate admissible orders on \(\mathbb{I} [0, 1]\) which is more general than those we find in the current literature. Also, we deal with the possibility of an admissible order on \(\mathbb{I} [0, 1]\) to be isomorphic to the usual order on \([0, 1]\). We prove that some orders constructed by our method are not isomorphic to the usual one and we make some considerations about the following question: is there some admissible order on \(\mathbb{I} [0, 1]\) isomorphic to the usual order on \([0, 1]\)?