According to this principle, a war cannot be just if it has not been authorized by the proper authorities. This may seem to make more sense in a medieval setting where one feudal lord might try to wage war against another without seeking the authorization of the king, but it still has relevancy today.
Granted, it is very unlikely that any particular general might try to wage war without some authorization from his superiors, but what we should pay attention to is who those superiors are. A democratically elected government which initiates a war against the wishes of (or simply without consulting) the populace (who, in a democracy, are sovereign like a king is in a monarchy) would be guilty of waging an unjust war.
The main problem with this principle lies in identifying who, if anyone, qualifies as the legitimate authority. Is it sufficient for a nations sovereign(s) to approve? Many think not and suggest that a war cannot be just unless it is initiated in accordance with the rules of some international body, like the United Nations. This might tend to prevent nations from going rogue and simply doing whatever they want, but it would also constrain the sovereignty of the nations who abide by those rules.
In the United States, it is possible to ignore the UN question and still be faced with a problem of identifying the legitimate authority: Congress or the President? The Constitution gives Congress the exclusive power to declare war, but for a long time now presidents have engaged in armed conflicts which have been wars in all but name. Were those unjust wars because of that?