Market share gains carved out by non-bank money transfer providers such as OFX, World First and TransferWise have belatedly raised some alarm at one of the major banks, with CBA deciding to slash its high fees for online transactions.Under a new fee schedule announced on Tuesday, CBA customers will pay an international money transfer fee of only A$6 on transfers under $1000 if they use the bank's online or mobile banking services.CBA previously charged a fee of $22 on such transactions.The bank will charge a flat fee of $12 on international transfers greater than $1000.Australian banks have been slow to respond to price competition in the money transfer market, choosing instead to treat the business activity as a high margin profit-spinner.   While CBA's fee adjustments will make it slightly more competitive against leading online providers such as TorFX and World First that charge no fees, the big test for the bank winning back market share will likely rest on the currency conversion rates it applies to transactions.Based on currency conversion offers shown on the NetBank website on Tuesday 24 October at 3pm, CBA remains an expensive provider.While OFX was offering to take Australian currency for US dollars at a rate of 77.3 US cents per A$1, CBA was only prepared to hand over 74 US cents.Those conversion rates mean that a CBA customer would receive $US 330 less than an OFX client when they each exchanged A$10,000 into US dollars.