Copyright © 2011 Boorapa Singha and Jintana Sanwong. This is an open access article distributed under the
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Suppose that is an infinite set with and is the symmetric inverse semigroup defined on . In 1984, Levi and Wood determined a class of maximal subsemigroups (using certain subsets of ) of the Baer-Levi semigroup dom and . Later, in 1995, Hotzel showed that there are many other classes of maximal subsemigroups of , but these are far more complicated to describe. It is known that is a subsemigroup of the partial Baer-Levi semigroup . In this paper, we characterize all maximal subsemigroups of when , and we extend to obtain maximal subsemigroups of when .