Last week Kenneth Clarke, the Chancellor, said that in principle stamp duty concessions could continue in the new market and he asked SIB to produce a consultation document outlining how firms could qualify for it.
The Government is prepared to accept a reduction in the pounds 1.2bn it receives from stamp duty and in the long term may phase it out altogether.
But a SIB consultation document indicated the intention was to produce a stamp duty regime that fitted the Stock Exchange, Tradepoint and any other trading services that might enter the London market.
SIB said: "Because this is a genuine consultation document we are considering the possibility that the way the Stock Exchange is thinking is not the most convincing."
The SIB consultation period finishes on 20 June, two weeks ahead of the Exchange's consultations on the new market, which began yesterday with the publication of detailed plans.
A key component of the Exchange electronic order book trading system will be a new category of firm called Registered Principle Traders who will be obliged to buy and sell stock to keep the market liquid, in return for certain benefits including stamp duty concessions.
These traders will take orders from customers on the telephone, but at prices set on a new electronic order book which will handle the top 100 stocks.
The order book replaces the market-making system by automatically matching buyers and sellers. But the Exchange has tackled the problem of how to keep the market ticking over when stock is short by suggesting the idea of registered traders who must step in to help when needed.
The key problem for SIB is drawing up a watertight definition of what makes a firm qualify for stamp duty relief that applies to any exchange.
It is considering alternatives to the registered trader proposal for maintaining liquidity at difficult times.