We say that a partial word w over an alphabet A is square-free if every factor xx' of w such that x and x' are compatible is either of the form lozenge a or a lozenge where lozenge is a hole and a is an element of A. We prove that there exist uncountably many square-free partial words over a ternary alphabet with an infinite number of holes. (c) 2008 Elsevier B.V. All rights reserved.