Deconstruction (amongst other things) attempted to “liberate the Other”. The problem is that there is an indefinite number of Others. Many Others are also at mutual odds.
Whatever the case is, surely only a shared language - the language that deconstruction rejected or deconstructed - can liberate the Other. As Thomas McCarthy puts it:
“Deconstruction can hardly give voice to the excluded other. The wholesale character of its critique of logocentrism deprives it of any language in which to do so.” 
That's why deconstruction couldn't even hint at anything directly political (rather than tangentially political) in any traditional sense. Hence the ineffable prose. This is McCarthy again:
“It is…merely by accident that his writings contain little analysis of political institutions and arrangements, historical circumstances and tendencies, or social groups and social movements, and no constructions of right and good, justice and fairness, legitimacy and legality?”
Isn’t it the case that ‘legality’, ‘legitimacy’, ‘fairness’, ‘justice’ - and nearly all the other concepts and words referred to by McCarthy - are essentially examples of “transcendental signifieds” in Derrida’s book (or "texts")? Thus Derrida's only interest in words/concepts (or at least his interest in political and philosophical positions) was to violently deconstruct them. If he hadn't done that, then the whole enterprise would have self-destructed (if not deconstructed) itself.
For instance, if Derrida had created a new concept of JUSTICE (if one can have a new version of an old concept), this would have been just another Derridean “centre” or “sign substitution”.
Even if a new concept for an old word were created, it would still be parasitical on the old concept (i.e., otherwise it wouldn't be a new concept for an old word).
That's why Marx wasn't just a “Left Hegelian”: he was also a Hegelian simpliciter. That's why “neo-Aristotelians” were Aristotelians simpliciter. Even an anti-Christian like Nietzsche was dangerously infected by - and parasitical upon - Christianity itself.
Perhaps the very notion of a new version of an old concept doesn't make sense. It may be better to call it a variation (or an elaboration rather than an equivalent). If we want a strict equivalent (or just an equivalent), then why not stick with the old concept?
An alternative to an old concept, however, is a different thing entirely. This might have been what Derrida was trying to do. If that were the case, then he could hardly use words like ‘fairness’, ‘right’, ‘legitimacy’ or any of the other words referred to by McCarthy above. Though if Derrida created an entirely new conceptual vocabulary (or a Wittgensteinian "private language"), then this would explain the difficulty in reading his work. Thus either he wasn't using traditional concepts at all; or he was creating new concepts (en masse). Alternatively, he perhaps used old words (which applied to old concepts) and applied new concepts to them. In that case, complications would multiply indefinitely.
It made Derrida's philosophy suspect and problematic when he used old words for alternative/new concepts. How would we know (as new readers) that this is what Derrida is actually doing? And if Derrida never gave definitions of his alternative concepts (which used old words), then we'd still be in the darkest of dark places.
Indeed Derrida couldn't even use the concept CONCEPT because that too belongs to the forbidden vocabulary of “traditional Western metaphysics” (as he often put it). Of course it may not even be possible to reject the concept CONCEPT and still do philosophy - or even write or speak at all (as the late Wittgenstein might have put it). Thus this was surely a rhetorical claim on Derrida’s part.
For a start, one must already have concepts to reject the concept CONCEPT. However, Derrida might have replied that he did indeed have the concept CONCEPT; though it was his job to reject or deconstruct it. Thus perhaps what he wrote was so far removed from traditional philosophy (of whichever kind) that he didn't even need the concept CONCEPT (or any other concept for that matter).
How far removed from philosophy - and indeed traditional language - can one be and still make sense and say something? Again, I can hear a Derridean reply: I'm not saying anything! This wouldn't be so far removed from Wittgenstein (in certain moods) and Heidegger who seemed to emphasise the point of pointlessness or the need to escape from traditional kinds of thinking. There's still a problem. What does non-statemental and non-conceptual philosophy look like? Is the answer simple? - It looks like Derrida’s philosophy and prose.
Writing itself (as seen conceptually in Derrida) needs to be overcome, rejected or deconstructed. The very thing that is WRITING is highly suspect and related to (amongst other things) ‘violence’. That's if we can call violence 'violence', it 'it', if...
Derrida, Jacques. (1973). Speech and Phenomena and Other Essays on Husserl's Theory of Signs.McCarthy, Thomas A. (1991) Ideals and Illusions: On Reconstruction and Deconstruction in Contemporary Critical Theory