If it wasn't for the loan, the parties could do this, though there would almost certainly be tax consequences (a taxable gain) either now or later (when the property is sold) to the one who received ownership for a nominal sum. (The difference between the value of that share of or interest in the property and the nominal sum paid for it would be the gain.)However, if the loan you are referring to is a standard mortgage, you cannot or alter ownership without paying off the loan; a change in ownership triggers the obligation to repay immediately. Check the mortgage papers to see if that is the case, but it is likely that you cannot do this while there is a mortgage, unless you also pay off or refinance (in the name solely of the remaining owner) the mortgage.