SAO PAULO -(Dow Jones)- Itau Unibanco SA (ITUB, ITUB4.BR), Brazil's largest private bank in terms of assets, said Monday it will keep its offer of 35 Brazilian reais ($18.61) for each outstanding share of credit-card networking-services company Redecard (RDCD3.BR), part of the bank's all-or-nothing bid to delist the company.

Last week, one of Redecard's minority shareholders, Lazard Asset Management Llc asked for a new independent evaluation of Redecard's shares. Lazard has a 9.82% stake in Redecard, while Itau has a total of 50.01% stake in the company.

But the bank said that it won't hike its offer and will retire the bid if the evaluation puts Redecard's share above BRL35.00.

Earlier this month, Itau Unibanco Chief Executive Roberto Setubal said the if the public tender offer fails, the bank will evaluate the possible sale of a portion or the bank's entire stake in Redecard.

The bank expects to acquire the 49.9% of Redecard that it doesn't already own. The offer will be completed only if two-thirds of outstanding shares are tendered in the offer. If the minimum level isn't met, Redecard will remain a publicly traded company.

The bank plans to hold the public tender offer to acquire Redecard's share in July or August.

-By Rogerio Jelmayer, Dow Jones Newswires; 55-11-3544-7071; rogerio.jelmayer@dowjones.com