The bill shifts responsibility for travel and accommodation of MPs and ministers away from the Speaker and Prime Minister to the Remuneration Authority plus an additional person with knowledge in the area.
The bill also sets in law a requirement by MPs to disclose their travel and accommodation costs quarterly, a practice instigated on a voluntary basis by Speaker Lockwood Smith.
And the bill contains what is known as the "Chris Carter clause" after the ex-Labour MP who went awol after his expulsion from caucus: it increases the penalty for being absent from Parliament without good cause from its present $10 a day to $270 a day.
Mr Finlayson acknowledged that the issue of travel and accommodation entitlements had caused the most public concern.
The bill would improve the independence in determining that support.
It recognised the need for members to be properly supported but maintained confidence in the integrity of Parliament.
The Speaker would continue to be responsible for setting allocations for party and member support funding, and the administrative, communications and support services for MPs and parties.
It passed its first reading and will be considered by the Government administration committee.