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4. The House may, if it thinks fit, on the passage trough the House of a bill that is deemed to be the same bill as a former bill sent to the Senate in the preceding session, suggest any amendments without inserting the amendments in the bill, and any such amendments shall be considered by the Senate and, if agreed to by the Senate, shall be treated as amendments made by the Senate and agreed to by the House; but the exercise of this power by the house shall not affect the operation of this section in the event of the rejection of the bill in the Senate.