Yes, your new basis in your IRA accounts is the previous basis minus the portion of prior DISTRIBUTIONS that weren't taxable on last year's form 1040.
Note that the IRS requires taxpayers to track the cost basis of their IRA accounts using Form 8606. If you have been tracking the cost basis, the adjusted basis is reported on line 14 of your last filed Form 8606.
If you have multiple IRA accounts, some funded with pre-tax money, and some funded with after-tax money, or a mixture of both, you can NEVER withdraw ONLY the nondeductible part - it must be prorated over the aggregate value of ALL Traditional IRA accounts.
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