At the time Mr Milosevic was President of Serbia and he had no intention of creating a potential rival.
Yugoslavia's new President, Vojislav Kostunica, has been in office for only a few days, but what can he hope to achieve in the longer term?
The post of Yugoslav president was invented by the now defeated previous incumbent, Slobodan Milosevic, following Yugoslavia's collapse in 1992.
At the time Mr Milosevic was President of Serbia and he had no intention of creating a potential rival.
Even when he transferred to the Yugoslav presidency in 1997 there was no formal increase in the president's authority.
Instead, Mr Milosevic continued to rule as a strongman who manipulated a network of contacts at all levels of the adminstration.
As a result, the powers of the federal Yugoslav president - or, indeed, those of the federal government - are relatively limited.
The president is commander-in-chief of the army but control over the police is in the hands of the Serbian and Montenegrin governments respectively.
Changes in Serbia
The federal government has few powers beyond dealing with foreign policy, foreign trade and monetary affairs.
The recent elections, which have brought victory to Mr Kostunica, have taken place only at the federal level.
The Serbian President, Milan Milutinovic - who is one of Mr Milosevic's closest associates - has two more years before his term runs out.
Serbian parliamentary elections will now be held later this year, leading to the formation of a new government to replace the current one - which is dominated by Mr Milosevic's Socialists and his wife's Yugoslav United Left.
Their coalition ally is the ultra-nationalist Vojislav Seselj, described by many Western officials as a fascist.
None of these are obvious partners for Mr Kostunica.
But the new president will also have to deal with potentially difficult allies at the federal level where a new government now needs to be formed.
The Montenegrin problem
Given the election results, the only way his bloc, the Democratic Opposition of Serbia, can form a government is by persuading the Montenegrin Socialist People's Party (SNP) - hitherto Mr Milosevic's close allies - to switch sides.
In the current fluid political situation, this obejctive appears quite possible - at least to the extent of attracting the majority of the SNP to back Mr Kostunica.
But success on this front would almost certainly alienate the SNP's opponents - Montenegro's Government under President Milo Djukanovic, which has built up a semi-independent state over the past two years in opposition to Mr Milosevic.
Most Montenegrins boycotted the elections because they felt, increasingly, that their interests had been violated by recent constitutional amendments.
And with barely a quarter of the electorate bothering to vote, Mr Kostunica's claim to represent Montenegro as part of Yugoslavia is open to dispute.
Kosovo
But if Mr Kostunica may have problems exercising his authority over Montenegro, he will have even greater difficulties in relation to Kosovo.
Barely 5% of the electorate - and virtually none of the majority ethnic Albanians - cast ballots there.
Under Mr Kostunica the Belgrade leadership will almost certainly be allowed a say in Kosovo's matters by the UN mission which currently administers Kosovo.
But as far as Kosovo's pro-independence local Albanian population is concerned, Mr Kostunica could just as well be the leader of a foreign country.
Mr Kostunica's greatest scope for action in the short term appears to be in international relations where he can begin to pull his country out if its isolation.
It is another question what country - or which parts of that country - he can genuinely represent, unless there are dramatic changes in Serbia, Montenegro and Kosovo to put more meaning into the term "Yugoslavia".