<?xml version="1.0"?><ownershipDocument><schemaVersion>X0201</schemaVersion>    <documentType>4</documentType><periodOfReport>2003-08-06</periodOfReport><notSubjectToSection16>0</notSubjectToSection16><issuer><issuerCik>0001016179</issuerCik><issuerName>DIAL CORP /NEW/</issuerName>        <issuerTradingSymbol>DL</issuerTradingSymbol></issuer><reportingOwner><reportingOwnerId><rptOwnerCik>0001173421</rptOwnerCik><rptOwnerName>THOMAS BARBARA S</rptOwnerName></reportingOwnerId><reportingOwnerAddress><rptOwnerStreet1>15501 NORTH DIAL BOULEVARD</rptOwnerStreet1><rptOwnerStreet2>SUITE 2212</rptOwnerStreet2><rptOwnerCity>SCOTTSDALE</rptOwnerCity><rptOwnerState>AZ</rptOwnerState><rptOwnerZipCode>85260-1619</rptOwnerZipCode><rptOwnerStateDescription></rptOwnerStateDescription></reportingOwnerAddress><reportingOwnerRelationship><isDirector>1</isDirector><isOfficer>0</isOfficer><isTenPercentOwner>0</isTenPercentOwner><isOther>0</isOther></reportingOwnerRelationship></reportingOwner><derivativeTable><derivativeTransaction><securityTitle><value>Phantom Stock Units</value></securityTitle><conversionOrExercisePrice><footnoteId id="F1" /></conversionOrExercisePrice><transactionDate><value>2003-08-06</value></transactionDate><deemedExecutionDate><value>2003-08-06</value></deemedExecutionDate><transactionCoding><transactionFormType>4</transactionFormType><transactionCode>A</transactionCode><equitySwapInvolved>0</equitySwapInvolved></transactionCoding><transactionTimeliness><value></value></transactionTimeliness><transactionAmounts><transactionShares><value>367.04</value></transactionShares><transactionPricePerShare><value>20.025</value></transactionPricePerShare><transactionAcquiredDisposedCode><value>A</value></transactionAcquiredDisposedCode></transactionAmounts><exerciseDate><footnoteId id="F2" /></exerciseDate><expirationDate><footnoteId id="F2" /></expirationDate><underlyingSecurity><underlyingSecurityTitle><value>The Dial Corporation Common Stock</value></underlyingSecurityTitle><underlyingSecurityShares><value>367.04</value><footnoteId id="F2" /></underlyingSecurityShares></underlyingSecurity><postTransactionAmounts><sharesOwnedFollowingTransaction><value>8255.16</value></sharesOwnedFollowingTransaction></postTransactionAmounts><ownershipNature><directOrIndirectOwnership><value>D</value></directOrIndirectOwnership></ownershipNature></derivativeTransaction></derivativeTable><footnotes><footnote id="F1">Security converts to common stock on a one-for-one basis.</footnote><footnote id="F2">On August 6, 2003, the reporting person acquired 367.04 phantom stock units at a price of $20.025 as a result of retainer and meeting fees paid under the Corporations Directors Deferred Compensation Plan.  Expiration date not yet known.</footnote></footnotes><remarks></remarks><ownerSignature><signatureName>Dianne B. Stoehr, Attorney-In-Fact</signatureName><signatureDate>2003-08-07</signatureDate></ownerSignature></ownershipDocument>

