In her weekly newsletter Zille said Zuma needed to match his "fine words in Parliament" with deeds.
"His pledge that the new executive will avoid being over-defensive, and that it will 'not view all criticism from the opposition in a negative light' suggests a welcome shift in attitude and approach," she said.
"If he is really committed to defending and protecting constitutionalism and the rule of law ? and many of his previous actions and statements cast grave doubt over his commitment ? he must match his fine words in Parliament with deeds."
She said the 77-strong DA caucus in Parliament would engage with the executive in a professional manner.
"We will not be adversarial for the sake of being adversarial. But we will be robust in opposing that which is bad for the country."
Zille suggested that Zuma follow five steps after he took office on Saturday.
First, he had to refuse to appoint "any of his cronies" to lead institutions whose independence was constitutionally enshrined, such as the National Prosecuting Authority, the police and the Constitutional Court.
Suspicions would be raised if Zuma appointed the acting head of the NPA, Mokotedi Mpshe, permanently in the position of National Director of Public Prosecutions.
"That would confirm suspicions that Zuma exerted political pressure on Mpshe to drop corruption charges against him on the eve of the election," she said.
Second, Zuma had to retract the statements he made shortly before the election, when he insinuated that judges should not be independent, but accountable to government.
Third, Zuma had to "prevail" on his colleagues in Cabinet to withdraw the draft Constitution 17th Amendment Bill, which empowered national government to usurp powers from local government.
"If the ANC manages to pass this constitutional amendment, giving itself a range of reasons to undermine local government, the ANC could effectively nullify voters' choice and enforce ANC policy from the centre ? even where the ANC loses power in municipal elections," Zille said.
Fourth, Zuma had to assure the public that his government would not attempt to revoke property rights to expedite land reform.
Finally, Zuma should not prevent the DA from making sure that "he has his day in court" to answer fraud and corruption charges.
"By dropping the charges against Zuma, the NPA created a precedent that individuals in positions of power are above the law and can bully their way out of trouble.
"Left unchallenged, this approach is the death knell for any constitutional democracy," Zille said.
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