ISA query

[rfn]

I currently have the following "savings"

C&G cash ISA - £4,500
Barclays Golden ISA - £2,000

I opened the Barclay's ISA during tax year 08/09. The money has been sitting in C&G since tax year 07/08. Barclays is paying 3.55% but the money is not earning much interest in C&G. Barclays ISA won't accept a transfer from C&G ISA.

Can I transfer the whole of C&G ISA to a better paying account, and then add money to the Barclays one (I can access that through my online banking so it's easier to add money to it), or is that not quite right?

Thanks in advance.