Centre-right leader Mirek Topolanek lacks an overall majority
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Czech Prime Minister Jiri Paroubek has stepped down, two-and-a-half months after elections left the country's parliament split down the middle.
The man who replaces him is Mirek Topolanek, leader of the right-of-centre Civic Democrats.
But Mr Topolanek's government does not have a majority, and will need the support of Mr Paroubek's Social Democratic Party in order to govern.
The Civic Democrats now have 30 days to win a confidence vote in parliament.
Correspondents say the Social Democrats are sending out mixed messages, and that their support may not be forthcoming.
Even if it is, it could be withdrawn at any time - possibly as early as the autumn. Then it will be back to square one.
Some believe Wednesday's appointment is merely the latest stage in a carefully staged-managed process, the culmination of which will be early elections and possibly electoral reform.
The country has survived 10 weeks of political limbo more or less intact, says the BBC's Rob Cameron in Prague.
But with some fairly crucial decisions looming on the horizon - including whether to host a US anti-missile base - the Czech Republic is in bad need of a government, he says.