The White House is reviewing whether to reform and potentially repeal a decades-old rule governing stock trading to ensure investors get better prices for their transactions.

The proposal to change the so-called trade-through rule was posted on the website of the Office of Management and Budget on Monday. The Securities and Exchange Commission adopted the current version of the rule in 2005, when now-Chairman Paul Atkins was commissioner there.

These measure exchanges, alternative trading systems and Citadel Securities or Vertu Financial Inc. such as prohibiting wholesalers from executing trades that ignore or “trade” the national best bid or offer, which has helped ensure that individual investors receive fair treatment.

Atkins opposed the move at the time. An SEC spokesman said Atkins noted in a 2005 dissent that it could have unintended consequences on the long-term development of financial markets.

The chairman previously said the trade-through rule forced brokers to focus only on the cost of executing trades, rather than other factors that contribute to whether investors got the “best execution” for their trades, such as speed or preferred trading venue.

“The subsequent fragmentation and increased costs of the trade-through rule have shown the integrity of Chairman Atkins, which is why he is calling on the Commission to reexamine the rule to avoid repeating the same mistakes made 20 years ago,” the spokeswoman said.

The rule changes could have far-reaching effects on many other aspects of the market structure, such as the rebates exchanges offer brokers for their business and the fee caps some exchanges impose on brokers for accessing their protected quotes.

It may take as long as the White House wants to review and edit the text of the proposed rule. Once it completes that process, the measure goes back to the SEC where commissioners, currently three Republicans on what is intended to be a bipartisan, five-person panel, must vote on it.

Once that’s done, the proposed rule will go out for public comment. The SEC incorporated the feedback into the final version of the rule, which must be voted on again by the Commission before it can take effect.