WARNING: THE EDGAR SYSTEM ENCOUNTERED ERROR(S) WHILE PROCESSING THIS SCHEDULE.
<TABLE> <S> <C>
<ARTICLE> 6
<RESTATED>
<CIK> 0000860937
<NAME> NUVEEN TAX-FREE UNIT TRUST
<SERIES> Series 606
<NAME> MICHIGAN INSURED TRUST
<NUMBER> 32
<MULTIPLIER> 1
<CURRENCY> U.S. DOLLARS
<FISCAL-YEAR-END> MAR-31-2000
<PERIOD-START> APR-01-1999
<PERIOD-END> MAR-31-2000
<PERIOD-TYPE> YEAR
<EXCHANGE-RATE> 1
<INVESTMENTS-AT-COST> 2,312,216
<INVESTMENTS-AT-VALUE> 2,391,143
<RECEIVABLES> 47,652
<ASSETS-OTHER> 0
<OTHER-ITEMS-ASSETS> 0
<TOTAL-ASSETS> 2,438,795
<PAYABLE-FOR-SECURITIES> 0
<SENIOR-LONG-TERM-DEBT> 0
<OTHER-ITEMS-LIABILITIES> 18,515
<TOTAL-LIABILITIES> 18,515
<SENIOR-EQUITY> 0
<PAID-IN-CAPITAL-COMMON> 0
<SHARES-COMMON-STOCK> 28,669
<SHARES-COMMON-PRIOR> 30,253
<ACCUMULATED-NII-CURRENT> 39,978
<OVERDISTRIBUTION-NII> 0
<ACCUMULATED-NET-GAINS> 41,372
<OVERDISTRIBUTION-GAINS> 0
<ACCUM-APPREC-OR-DEPREC> 78,927
<NET-ASSETS> 2,420,280
<DIVIDEND-INCOME> 0
<INTEREST-INCOME> 182,406
<OTHER-INCOME> 0
<EXPENSES-NET> 4,352
<NET-INVESTMENT-INCOME> 178,054
<REALIZED-GAINS-CURRENT> 12,750
<APPREC-INCREASE-CURRENT> -116,524
<NET-CHANGE-FROM-OPS> 74,280
<EQUALIZATION> 0
<DISTRIBUTIONS-OF-INCOME> 204,158
<DISTRIBUTIONS-OF-GAINS> 526,498
<DISTRIBUTIONS-OTHER> 0
<NUMBER-OF-SHARES-SOLD> 35,000
<NUMBER-OF-SHARES-REDEEMED> 6,331
<SHARES-REINVESTED> 0
<NET-CHANGE-IN-ASSETS> -804,423
<ACCUMULATED-NII-PRIOR> 66,082
<ACCUMULATED-GAINS-PRIOR> 28,622
<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>
