I just filed my personal tax return. I want to file taxes for a small business I own. But I don't see any link how to start new tax filing after personal tax filing.

[ee-ea]

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[VolvoGirl]

Unless you are self employed or a Single Member LLC or sole proprietor you need to file a separate Business return.  

If you need to file a separate Business return like for a 1065 Partnership or LLC or a 1120 including a Single Member LLC - S corp or a 1041 Estate/Trust return you need Turbo Tax Business in addition to a personal tax program.

You need to buy Turbo Tax Business, not to be confused with the personal Home & Business version. Home & Business is just for personal returns that need schedule C for self employment. TT Business is not available to do online or on a Mac. You can buy the Windows Desktop program here,
https://turbotax.intuit.com/small-business-taxes

IF YOU DO NOT NEED to file a Business return you needed to add the small business to your personal return on schedule C.  Either way you need to amend your personal return to add a schedule C or to add a K-1 or W2 you get from the Business return.  You should prepare the Business return before your personal return.