WARNING: THE EDGAR SYSTEM ENCOUNTERED ERROR(S) WHILE PROCESSING THIS SCHEDULE.
<TABLE> <S> <C>
<ARTICLE> 6
<RESTATED>
<CIK> 0000883073
<NAME> NUVEEN TAX-FREE UNIT TRUST
<SERIES> Series 736
<NAME> NATIONAL INSURED TRUST
<NUMBER> 271
<MULTIPLIER> 1
<CURRENCY> U.S. DOLLARS
<FISCAL-YEAR-END> MAY-31-2000
<PERIOD-START> JUN-01-1999
<PERIOD-END> MAY-31-2000
<PERIOD-TYPE> YEAR
<EXCHANGE-RATE> 1
<INVESTMENTS-AT-COST> 5,451,071
<INVESTMENTS-AT-VALUE> 5,719,091
<RECEIVABLES> 144,640
<ASSETS-OTHER> 0
<OTHER-ITEMS-ASSETS> 0
<TOTAL-ASSETS> 5,863,731
<PAYABLE-FOR-SECURITIES> 0
<SENIOR-LONG-TERM-DEBT> 0
<OTHER-ITEMS-LIABILITIES> 111,822
<TOTAL-LIABILITIES> 111,822
<SENIOR-EQUITY> 0
<PAID-IN-CAPITAL-COMMON> 0
<SHARES-COMMON-STOCK> 56,564
<SHARES-COMMON-PRIOR> 61,915
<ACCUMULATED-NII-CURRENT> 30,165
<OVERDISTRIBUTION-NII> 0
<ACCUMULATED-NET-GAINS> 168,147
<OVERDISTRIBUTION-GAINS> 0
<ACCUM-APPREC-OR-DEPREC> 268,020
<NET-ASSETS> 5,751,909
<DIVIDEND-INCOME> 0
<INTEREST-INCOME> 364,332
<OTHER-INCOME> 0
<EXPENSES-NET> 10,856
<NET-INVESTMENT-INCOME> 353,476
<REALIZED-GAINS-CURRENT> 40,833
<APPREC-INCREASE-CURRENT> -396,732
<NET-CHANGE-FROM-OPS> -2,423
<EQUALIZATION> 0
<DISTRIBUTIONS-OF-INCOME> 356,314
<DISTRIBUTIONS-OF-GAINS> 0
<DISTRIBUTIONS-OTHER> 0
<NUMBER-OF-SHARES-SOLD> 75,000
<NUMBER-OF-SHARES-REDEEMED> 18,436
<SHARES-REINVESTED> 0
<NET-CHANGE-IN-ASSETS> -906,670
<ACCUMULATED-NII-PRIOR> 33,003
<ACCUMULATED-GAINS-PRIOR> 127,314
<OVERDISTRIB-NII-PRIOR> 0
<OVERDIST-NET-GAINS-PRIOR> 0
<GROSS-ADVISORY-FEES> 0
<INTEREST-EXPENSE> 0
<GROSS-EXPENSE> 0
<AVERAGE-NET-ASSETS> 0
<PER-SHARE-NAV-BEGIN> 0
<PER-SHARE-NII> 0
<PER-SHARE-GAIN-APPREC> 0
<PER-SHARE-DIVIDEND> 0
<PER-SHARE-DISTRIBUTIONS> 0
<RETURNS-OF-CAPITAL> 0
<PER-SHARE-NAV-END> 0
<EXPENSE-RATIO> 0
[AVG-DEBT-OUTSTANDING] 0
[AVG-DEBT-PER-SHARE] 0
</TABLE>
