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The Republican Movement is calling for governors-general to be appointed only if three-quarters of parliament agrees.
Parliament's government administration committee is considering the Governor-General Bill. The Bill aims to update language and remove outdated measures following a Law Commission review which found provisions in the Civil List Act were old-fashioned, unnecessarily complicated, and no longer suited to supporting the office of a modern governor-general.
The recommendations would be implemented in time for the next governor-general to assume office in August next year.
Republican Movement chairman Lewis Holden said a range of names, including that of Sir Don McKinnon, had been raised as potential candidates.
The process for the next appointment should be open and transparent and the myth that the opposition was consulted should be changed so there was a formal requirement, he said.
The movement suggested a three-quarter majority plus support of at least half the party leaders, to ensure that small parties views were counted.
"Basically, the whole point is to make sure that person is as absolutely neutral as possible."
National's Nikki Kaye raised concerns that there could be several one-member parties in Parliament, which could give them too much power if an appointment was based on one vote per leader.
Mr Holden said the method would ensure appointments were made that most MPs and parties found acceptable.
He also said the term of office needed to be legislated and highlighted the "frankly ridiculous" provision that the new Governor-General got paid six months before taking office - a hangover from colonial days.
"That's basically so once you step on a boat at Southampton dock you start getting paid as Governor-General of New Zealand, so obviously, that raised questions about what their term should be."
Changes in the Bill would see:
* The Governor-General's salary income tax exemption removed but double severance pay to six months' salary.
* Some restrictions on the availability of the annuity paid to former governors-general and their surviving spouses or partners. The annuity recognised the role the governor-general's spouse or partner played and would not continue to be available if a surviving spouse or partner remarried or entered a new relationship, or if a former governor-general and surviving spouse or partner chose to live overseas.
Some benefits would be carried over, such as domestic travel and the use of chauffeur-driven cars - similar to benefits former prime ministers get to recognise public demands could continue after the person leaves office.
The Bill would also create a new funding structure for the Office of Governor-General.