<?xml version="1.0"?>
<ownershipDocument>

    <schemaVersion>X0202</schemaVersion>

    <documentType>3</documentType>

    <periodOfReport>2007-11-01</periodOfReport>

    <noSecuritiesOwned>0</noSecuritiesOwned>

    <issuer>
        <issuerCik>0001399315</issuerCik>
        <issuerName>NEW M&amp;I CORP</issuerName>
        <issuerTradingSymbol>MI</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001187361</rptOwnerCik>
            <rptOwnerName>MELLOWES JOHN A</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>770 NORTH WATER STREET</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>MILWAUKEE</rptOwnerCity>
            <rptOwnerState>WI</rptOwnerState>
            <rptOwnerZipCode>53202</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeHolding>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>2000</value>
                    <footnoteId id="F1"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value></value>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeHolding>
        <nonDerivativeHolding>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>1200</value>
                    <footnoteId id="F1"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>By Trust</value>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeHolding>
        <nonDerivativeHolding>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>7971.522</value>
                    <footnoteId id="F1"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>By Deferred Compensation Plan</value>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeHolding>
    </nonDerivativeTable>

    <footnotes>
        <footnote id="F1">Reflects the acquisition of shares of common stock of the Issuer pursuant to a series of transactions under an Investment Agreement, dated as of April 3, 2007, among the entity formerly known as Marshall &amp; Ilsley Corporation (&quot;Old M&amp;I&quot;) (which was subsequently converted to a limited liability company and renamed M&amp;I LLC and is a subsidiary of the Issuer), certain of its subsidiaries and WPM, L.P. (the &quot;Investment Agreement&quot;).  Pursuant to the Investment Agreement, on November 1, 2007, Old M&amp;I merged with one of its subsidiaries to effect the formation of a holding company to hold all of the outstanding stock of Old M&amp;I (the &quot;Holding Company Merger&quot;).  As a result of the completion of the transactions contemplated by the Investment Agreement, each holder of Old M&amp;I common stock as of the effective time of the Holding Company Merger received three shares of common stock of the Issuer (which was subsequently renamed Marshall &amp; Ilsley Corporation) and one share of common stock of Metavante</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ Jodi W. Rosenthal (pursuant to Power of Attorney filed herewith)</signatureName>
        <signatureDate>2007-11-05</signatureDate>
    </ownerSignature>
</ownershipDocument>
