The Scottish National Party is to temporarily lose its one-seat advantage at Holyrood.
Ms Constance is expecting her first child in the autumn
The Nationalists' voting power in the Scottish Parliament will be cut when Livingston MSP Angela Constance takes maternity leave.
The SNP said it was delighted for the newly-elected MSP, who is expecting her first child in the autumn.
Her victory in Livingston was an SNP gain from Labour. Her absence means the SNP will lose its one-seat lead.
Even with support from the Greens and either the Liberal Democrats or the Conservatives, the SNP government would be one vote short of a majority at Holyrood.
The situation could leave Independent MSP Margo Macdonald in a particularly powerful position.
However, First Minister Alex Salmond has insisted his minority administration would not be crippled by the looming loss of its one-seat majority over Labour.
"I am quite certain that whatever differences we have with the other political parties, none of them would want to take advantage of Angela's maternity leave in order to cause difficulties for our administration," he told BBC Radio Scotland's Good Morning Scotland.
"I don't think our political opponents will stoop that low. If there are difficulties we will work our way through them.
"As a government which has to command a majority by persuasion and argument, we will just have to persuade and argue all the more forcibly."
If the Scottish Parliament used a pairing system then it would mean an MSP from the opposition would not vote while Angela Constance was away.
However, the SNP withdrew from a pairing system a few years ago so it now will be a vote down while she is on maternity leave.