Bradford Council has ordered its 150 schools to switch millions of pounds of deposits with Yorkshire Bank to a bigger bank because of its fears about the banking sector.
In a letter to the schools seen by the city's Telegraph & Argus newspaper, council executive Andrew Redding said Yorkshire Bank held two-thirds of school budget cash balances and there had always been a successful relationship with the council.
But he warned that because of "continuing turbulence in the banking sector" finance bosses had decided funds should only be held with the four largest UK clearing banks, Barclays, HSBC, Lloyds TSB and RBS (NatWest).
While telling schools there was "no need to panic", Mr Redding says of the Yorkshire: "The current rating and size of this bank means that this bank does not comply with the council's treasury management policy."
He said the aim was to evenly distribute the school balances across all of the big four banks.
A spokesman for Clydesdale Bank said it would have a "negligible effect" on Yorkshire Bank business .
They added: "We remain part of one of the largest and safest banking groups in the world and believe we are a good home for anyone's savings."