You can delete the search that you have shared.
Procedure
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From the My Applications page in the Web Console, go to Monitoring > Log Monitoring.
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At the top of the page, click Search.
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Below the search bar, click Show History to show the Shared Search table.
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On the Shared Search page, click Shared By Me to list the shared searches.
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To delete the shared search, hover the cursor over the appropriate shared search, click the delete icon, and then click Yes to confirm the deletion.
Results
The shared search is deleted from the users Shared By Me table.