Yulia Tymoshenko is refusing to go despite requests from the new president
By Dariya Merkusheva
BBC News, Ukraine
Ukrainian Prime Minister Yulia Tymoshenko withdrew her appeal case against the elections results from the Supreme Administrative court and the court has closed the case. But she has not conceded.
She said once again that Viktor Yanukovych will never be considered Ukraine's legitimately elected president.
This is in stark contrast to her fellow Orange Revolutionary - incumbent Ukrainian President Viktor Yushchenko.
On Saturday he finally congratulated his long-time rival, Mr Yanukovych, on a legitimate victory.
Sergei Mishchenko, an MP from Mrs Tymoshenko's party, has said their party is planning to boycott the inauguration ceremony scheduled for 25 February.
He also added Mrs Tymoshenko is not giving in, she will not recognise the elections results and she will continue to work as prime minister.
Mr Yanukovych has asked Mrs Tymoshenko to step down from her post on several occasions. And she has said that she will not.
President-elect Yanukovich's Regions Party might seek a new coalition
As president, Mr Yanukovych does not have the right to fire or to appoint a prime minister - that is up to Ukraine's parliament.
At the moment Mrs Tymoshenko's party is still part of the parliamentary coalition, but negotiations are under way to form a new coalition based on Mr Yanukovych's Regions Party.
One of the leaders of the Regions Party, Nikolai Azarov, speaking to Ukrainian TV channel Inter, said it was fantastic to even consider the possibility of Mrs Tymoshenko remaining in her post for much longer.
But no-one here in Ukraine thinks it will be an easy task to remove her.
Country in limbo
Once MPs form a new coalition they are likely to vote Mrs Tymoshenko's government out, but until a new government is formed - and that can take weeks in the current political situation - Mrs Tymoshenko will remain as acting prime minister under President Yanukovych.
Analysts agree that little will be achieved in those weeks, and the country will remain in limbo.
Of course, these coalition talks depend on many factors, on internal politics and favours.
If they fail, Ukrainians will have to vote once again - in early parliamentary elections.
Either way, despite peoples' hopes, the economic situation is not likely to improve drastically.
Last year the country's economy shrank by 15%.
Mr Yanukovich vowed to unite the country
Mr Yanukovych has promised to improve the lives of those most disadvantaged - state workers and pensioners.
During his election campaigning he also promised to create more jobs.
But with a government run by his rival he will experience difficulties in fulfilling any of his promises.
Mrs Tymoshenko will also not be able to push any of her priorities.
The country is still living according to last year's budget. It is even unclear where the money for the inauguration is to come from.
Ukraine is also waiting for the much needed last tranche of the $16.4bn (£10.6bn) bailout programme from the International Monetary Fund.
This payment was suspended last year - until after the presidential elections - with a specific demand from the IMF for political stability and a democratic transfer of power.
However, Mr Yanukovych will have to consider what his rival stands for. Nearly half the country did, after all, vote for Mrs Tymoshenko, and he won by a small margin.
He promised to unite the country - the Russian-speaking east and south that backed him overwhelmingly, and the Western Ukrainian-speaking half that backed Mrs Tymoshenko.
But no-one is really certain how he will achieve that.
Just after the elections Mr Yanukovych said he was still undecided whether to visit Russia or an EU country first, but now the Kremlin is saying Mr Yanukovych will go to Moscow in early March.
There are no announcements about a visit to a Western European capital yet.