When you posted your question, you indicated that you are using the CD or download TurboTax software. If so, you should be able to deduct alimony you paid in any edition, including Basic, which is what you said you are using.
If you are using TurboTax Online, you cannot deduct alimony in the Free Edition because the deduction for alimony requires Form 1040. Free Edition supports only Forms 1040EZ and 1040A, not Form 1040. Alimony cannot be deducted on Form 1040EZ or Form 1040A. The next step up from Free Edition is Deluxe.