Legal analysis: No, if the house is mortgaged, then the house is mortgaged to the bank. Housing Authority stipulates that mortgaged houses cannot be registered for property right transfer. If you have a mortgage, you can't add a name. If you want to cancel the mortgage, you need the consent of the bank. For banks, lenders will not cancel their mortgages without paying them off. Real estate mortgage refers to the behavior that the property owner takes the house deed as the mortgage to obtain the loan and pay the interest on schedule.

Legal basis: Article 406 of the Civil Code of People's Republic of China (PRC), during the mortgage period, the mortgagor may transfer the mortgaged property. Unless otherwise agreed by the parties, such agreement shall prevail. If the mortgaged property is transferred, the mortgage right will not be affected. Where the mortgagor transfers the mortgaged property, it shall promptly notify the mortgagee. If the mortgagee can prove that the transfer of mortgaged property may damage the mortgage right, he may request the mortgagor to pay off the debt in advance or deposit the proceeds from the transfer with the mortgagee. The part of the transfer price exceeding the amount of creditor's rights belongs to the mortgagor, and the insufficient part is paid off by the debtor.