Mr Olmert denies all the corruption allegations against him
Israeli police have closed one of the criminal investigations against Prime Minister Ehud Olmert's for lack of evidence, a police spokesman said.
The probe was into his purchase of a house in Jerusalem significantly below market price while mayor of the city.
"The head of the investigation team reached the conclusion there isn't concrete evidence of any illegal act," police spokesman Micky Rosenfeld said.
Mr Olmert denies wrongdoing, though a series of probes caused him to resign.
The 63-year-old, who only has days left in office, still faces possible indictment on charges of fraud and breach of trust.
EHUD OLMERT'S POLITICAL LIFE
1993: Begins 10-year stint as mayor of Jerusalem
2005: Leaves right-wing Likud party with former Prime Minister Ariel Sharon to form Kadima
2006: Takes over as leader when Ariel Sharon suffers a stroke
2007: Helps re-launch Israeli-Palestinian peace talks after seven-year hiatus
2008: Announces plans to resign
In the so-called Cremieux property case, Mr Olmert paid $325,000 less than market value for the property in question, which led to suspicions of fraud and bribery.
In December, he was cleared because of lack of evidence of corruption in the privatisation of an Israeli bank while he was finance minister in 2005.
However, he may face charges over separate allegations, including for claiming extra expenses on trips abroad, unlawfully accepting cash from a US businessman and for corrupt political appointments.
Police have already recommended he be indicted in the first of two of these three cases.
Mr Olmert remains in office while his designated successor, Likud leader Benjamin Netanyahu, builds a new government following elections in February.
Correspondents say allegations of corruption have swirled around Olmert throughout his three-decade political career, but he has never been convicted of a crime.