No,you do not get any deduction by giving any gift to a relative.If your income is otherwise taxable,you have to pay your tax first and then out of net receipts only can you give a gift.Your relative may not be taxed on the amount you are giving the gift but there will not be any difference in your tax liability.In fact if you give a gift to your spouse or minor child,the income therefrom,if any,will be clubbed in your hands and will be taxed as your income.