An *unbordered* word is a string over a finite alphabet such that none of its proper
prefixes is one of its suffixes. In this paper, we extend results on unbordered words to
unbordered partial words. Partial words are strings that may have a number of “do
not know” symbols. We extend a result of Ehrenfeucht and Silberger which states that
if a word *u* can be written as a concatenation of nonempty prefixes of a word *v*, then
*u* can be written as a unique concatenation of nonempty unbordered prefixes of *v*. We study properties of
the longest unbordered prefix of a partial word, investigate the relationship between
the minimal *weak* period of a partial word and the maximal length of its unbordered
factors, and also investigate some of the properties of an unbordered partial word
and how they relate to its critical factorizations (if any).

*Keywords*: Words, partial words, unbordered words, unbordered partial words.