The Ibrox club last month had agreed two 'short-term credit facilities' for £1.5m, one with Laxey and the other £500,000 from director Sandy Easdale.
However, it has now emerged that the deal with Laxey has been transferred to shareholder and lifelong Light Blues fan Letham.
The deal is for the same amount but it's understood the repayment premium is at a reduced rate of £45,000 instead of the reported £150,000 on the previous deal with the Isle of Man-based consortium. The interest-free agreement with Easdale remains as it is.
A Rangers statement to the Stock Exchange read: "On 24 February 2014, the Company announced that it had entered into two secured short term credit facilities for an aggregate amount of up to £1.5 million.
"These credit facilities were provided by Laxey Partners Ltd ("Laxey") to the amount of £1 million (the "Laxey Facility") and Alexander Easdale to the amount of £500,000 (the "Easdale Facility").
"Laxey has, pursuant to an agreement entered into today, transferred all rights and obligations in relation to the Laxey Facility to Mr George Letham including all its rights in relation to the standard security granted as security for the Laxey Facility. Mr Letham is a shareholder in the Company and a lifelong Rangers fan.
"The Laxey Facility, now transferred by Laxey to Mr George Letham, remains subject to the same terms and conditions with the exception that the premium payment has been reduced to £45,000 and remains payable in shares or cash."