Livni's failure to assemble a ruling coalition for Kadima last year triggered Tuesday's elections.
He had broken with the Likud and set up a new, centrist party, Kadima.
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By that point, Ms Livni may find herself competing with other Kadima heavyweights for the leadership.
But Kadima positions itself as a centrist alternative and has attracted prominent members of both camps.
He then left to form the centrist party, Kadima, taking prominent moderates with him.
In its brief political life span, Kadima's membership rolls have been subject to multiple criminal investigations.
He wants Mr Netanyahu to swap his hardline partners for Tzipi Livni's centrist Kadima party.
In condemning Netanyahu, Livni and her Kadima colleagues were energetically assisted by the Israeli media.
They have repeatedly threatened to pull their support of Netanyahu should he adopt Kadima's position.
In her belief that all ends justify the means, Livni is a loyal representative of Kadima.
If Netanyahu wants a leftist party in his government, he will need to bring in Kadima.
He tells us that the difference between Kadima and Likud is one of tone, not substance.
Kadima's purpose in this, it was argued, was to lower the public's support for Netanyahu.
Key figures, including Israel's president, Shimon Peres, and the Knesset's speaker, Dalia Itzik, are now in Kadima.
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Kadima officials cautioned that the party is in its infancy, and its platform may grow and change.
Then, as elections approached, Kadima declared that deterrence had been achieved and pulled IDF forces from Gaza.
"Tonight, Kadima has decided to withdraw from the national unity government, " Mofaz told reporters after the meeting.
KADIMA'S INTERESTS as a political party place it at loggerheads with the government on almost every issue.
Yitzhak Mordechai formed the ill-fated Center Party in 1999, and Sharon formed the centrist Kadima Party in 2005.
Mr Mofaz's Kadima has 28 seats in parliament to the 27 held by Mr Netanyahu's lot, the Likud.
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Livni took over as Kadima leader after Prime Minister Ehud Olmert stepped down from the post amid corruption investigations.
The ruling Kadima Party won the most seats in the Knesset, Israel's parliament.
Kadima, which is the Hebrew word for forward is now under the leadership of acting Prime Minister Ehud Olmert.
For evidence of this demoralization, one need only look to the Kadima Party.
Kadima se ha quedado con 12 ministerios, incluyendo el cargo de primer ministro.
Last Friday it was disclosed that on Wednesday afternoon, Netanyahu had reopened coalition talks with Kadima leader Tzipi Livni.
It was his hope that as the odd man out, Kadima would be destroyed as a viable political entity.
But his only option for beating Livni in the Kadima leadership primary is to outflank her on the Left.
But he returned to the Likud leadership later that year following Sharon's break with the party to form Kadima.
However, some cautioned that this initial euphoria for Kadima was likely to cool.
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