Professor Trelawney had not been driven out of Hogwarts.
Although Umbridge had cited Educational Decree Number Twenty-Three to assert her right to dismiss teachers, Dumbledore had left her powerless with a single sentence.
Although the High Inquisitor had the authority to dismiss the school's teachers, she had no authority to expel them. That right remained with the Headmaster of Hogwarts, Dumbledore.
Umbridge was somewhat dissatisfied with this, but that was how things stood. At least, for the time being.
Besides, by dismissing Trelawney, she had made everyone at the school take her power and authority seriously once more, achieving her objective. Trelawney therefore accepted this outcome for the time being.
But just as Harry and the others thought the matter had been settled for now, something else happened.
With Trelawney dismissed, the school clearly needed another Divination professor.
Dumbledore seemed to have prepared for this well in advance. He brought in a centaur, one Harry knew.
It was Firenze, the centaur with silver hair and a horse's body.
Harry still remembered that this was a centaur who could use what appeared to be magical abilities, when no previous records or literature had ever mentioned centaurs being able to use magic.
Just as Harry and the others were thinking that Divination might become a little more interesting, Umbridge-or rather, the Ministry of Magic behind her-actually made another move.
On the grounds that the school governors unanimously opposed nonhuman wizards serving as professors, they blocked Firenze's appointment as the Divination professor.
And when Dumbledore stated that there were no more wizards in the United Kingdom with useful Divination abilities, Umbridge smiled smugly.
Yes, Umbridge had the authority to dismiss unqualified professors.
Although the people she wanted to dismiss were probably more likely to be Professor McGonagall and the others, she certainly did