UPDATE 3-RBS agrees 9.7 mln stg CEO pay deal

* CEO could get 6.4 mln stg in share options

* Unite union condemns pay deal

* Shares close down 3.4 pct (Adds company confirmation, updates package value, share price)

LONDON, June 22 (Reuters) - Stephen Hester, the head of part-nationalised lender Royal Bank of Scotland (RBS.L), is to get a pay package potentially worth more than 9.7 million pounds ($15.98 million), the company said on Monday.

The maximum payout would include share awards of about 6.4 million pounds achievable only if performance targets, including a near-doubling of RBS' share price to 70 pence, were met.

Chairman Philip Hampton said the package meant Hester's financial interests were linked to those of shareholders.

"Over the last few months we have been consulting with shareholders on the most appropriate way to incentivise and reward RBS's Chief Executive, Stephen Hester," Hampton said in a statement.

"We now have support for a remuneration plan that ensures the majority of Stephen's reward is non cash and based on his performance."

The Unite trade union said the package was inappropriate given recent large-scale job losses at RBS and other banks.