Royal Bank of Scotland is under fire over new bonus schemes for its chief executive, Stephen Hester, and other top bankers amid concern about the performance criteria attached to multimillion-pound awards by a bank 70% owned by the taxpayer.

The latest controversy follows the award of shares worth £5m to four RBS bankers last week. The largest award was to Ellen Alemany, who runs the bank's US business and was given almost 6m shares, worth £2.4m based on Friday's closing price of 41p. Three other bankers had awards of about 1.8m shares each, worth about £750,000 at current share prices.

The shares were awarded during an ongoing review of the pay structure for Hester, parachuted in as chief executive when Sir Fred Goodwin was ousted last year. Goodwin's pension of £700,000 a year continues to cause controversy.

City institutions being consulted about the scheme for Hester, who earns £1.2m a year, are determined that strict performance criteria are attached. One investor said: "People are not entirely happy [about the deal for Hester] and have asked them to refine it. Its performance criteria are not sufficiently stretching. They have been told to think again."

According to disclosures to the stock exchange, the four bankers issued with shares will not be able to cash in their awards for three years and only if certain performance criteria are reached.

The awards – also made to top bankers Alan Dickinson, Chris Sullivan and Ron Teerlink – are also subject to "clawback", which allows the bank to reclaim any payments for profits that turn sour later on.

But details of the performance criteria have not been released, largely because the bank is undergoing a dramatic overhaul, led by Hester, which is still being devised and has already led to 9,000 job cuts. Vince Cable, the Liberal Democrat Treasury spokesman, called the awards "completely unjustified" and "utterly unacceptable".

RBS indicated it would make the criteria public later on. A previous incentive scheme has not paid out since 2004.

Hester's pay deal is also being finalised, along with a scheme for outgoing finance director Guy Whittaker and his replacement. It is thought a number of structures are being considered in addition to traditional awards of shares. RBS is also thought to be looking at a pay deal that might include subordinated debt.

Subordinated debt was first introduced as a way of paying RBS bankers after the row in February over a £1bn bonus payout for its staff. UK Financial Investments, the body that controls the taxpayer's stake in the bank, reduced the cash bonuses to £340m but allowed other payments to take place in less conventional forms, such as subordinated debt, and over a three-year period.

Hester, who has a "no reward for failure" clause in his contract, has warned that RBS has lost top staff as a result of the clampdown on bonuses despite the share awards being made to some bankers. Among RBS bankers to have received share awards this year is John Hourican, head of global banking and markets, who has been granted 21.3m shares and 7.4m options, a package currently estimated to be worth £11m.

An RBS official said: "We have put in place a new leadership team to lead RBS through the substantial restructuring we have under way. It is critical that executive reward is made dependent on the delivery of those plans over the next three to five years to align their interests directly with those of our shareholders. These incentives are designed to do just that and there will be no reward for failure. Nothing will be paid until and unless performance criteria are achieved, and awards are subject to clawback.

"All such incentives will have exacting performance criteria attached to them based on delivery against our objectives. It is the group's intention to outline corporate and divisional business targets upon completion of our strategic review this summer. These targets will form the basis of all long-term incentives."