Change to working hours - new contract required?

Would anybody know the answer to this please...

A company offers reductions in hours to all staff willing to reduce their contracts, hoping some will take them up and save them money.
Staff member goes for it and changes from working 5 days (full time) to three days.
Should the staff member be given another contract of employment?

I thought they should....but have no legal / employment background.

Would appreciate any advice, thanks.

Just in case my question was not totally clear:

Employee holds a paper contract saying their job is 5 full days a week, and salary is X amount. Job has now been changed to three full days per week - should a new paper contract be issued stating this, with new salary?

Thanks!

Not necessarily a contract, but I would expect something in writing (eg a letter) from the employer outlining what the changes are and for the employee to sign it snd return it saying they've agreed