Credit Suisse puts bigger value on Brazil's Redecard

* Gives higher estimate for card processor's worth

* Itau Unibanco buyout offer at lower end of est'd worth

* Redecard shareholders could now seek sweetened offer

RIO DE JANEIRO, June 15 (Reuters) - Credit Suisse estimated on Friday that Brazilian card payment processor Redecard was worth 34.66-38.12 Brazilian reals ($16.95-$18.65) per share, putting a buyout offer by local bank Itau Unibanco at the lower end of that range.

The valuation was higher than the estimate of 34.18-37.59 reais by international financial adviser Rothschild, commissioned by Itau Unibanco, but which had been disputed by Redecard stakeholder Lazard Asset Management.

Itau Unibanco said in March it was prepared to pay 35 reais per share to buy the company and said later it would withdraw its offer if the upper end of any new valuation was higher than that amount.

The higher valuation from Credit Suisse may now encourage Redecard shareholders to push for a sweetened offer.

($1 = 2.0444 Brazilian reals) (Reporting by Fabio Couto; Writing by Peter Murphy; Editing by Gary Hill)