Can we refinance our second mortgage?

We bought a house last year with two mortgages. Because we only put down 10% for the loan, having the second mortgage of 10% of the loan, this way we don’t have to pay for the insurance. This second mortgage has an interest rate of 9.75% while our other mortgage is at 6%. We want to refinance this second mortgage to a lower rate. Can we do that? Is there anything that preventing us from refinance just this second mortgage? There is no early payment (repayment) penalty on both of our mortgages. Thank you very much for your help.

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