My aim in this paper is to clarify Aristotle's concept of matter, which has been misunderstood, I think, by many scholars. Some commentators insist that Aristotle believes in Prime matter, an ultimate subject with no determinate property in itself. One of the main resources that support such a viewpoint is the passage quoted in the next page. In this quote Aristotle undertakes what scholars metaphorically call "stripping-away", an operation designed to uncover an ultimate subject which underlies all properties of a thing. The uncovered entity is in itself neither something (τι) nor of a certain quantity (ποσον)) nor assigned to any other of the categories by which being is determined. Jan Lukasiewicz even says that this passage is an ancestor of doctrines broadly determined as the bare substratum theory. However it seems to me that such interpretations are incorrect, or at least may lead to a serious misconception of Aristotelian matter. Now agreeing with the recent commentators who deny the fact that prime matter is the main focus of Z3, I am still unsatisfied with the interpretations on this specific passage carried out by them. The reason is that people seems not fully aware of the historical background of Aristotle's argument: ancient materialists held that no matter what changes may occur to things, there must be an underlying subject which persists as the same, determinate entity, that is, a simple, permanent element of all complex, changeable things. I intend to argue that Aristotle presents his own conception of matter by criticizing such materialistic view, which I think is the point of his argument in the given passage.