Delete A Relationship
To delete an FK, select a table from the Object Browser,
1) Click on "Relationships/Foreign Keys" icon, or
2) Right click on the table(in the Object Browser) and select the menu option "Relationships/Foreign Keys", or
3) Press F10 key.
This opens up an Alter Table tab with the focus on Foreign Keys sub tab.
Click on Delete button in the toolbar to delete the selected relationship.
Before MySQL/InnoDB-4.0.13, MySQL does not provide you with a one-query-method to delete a FK. MySQL and InnoDB docs suggest dropping the table and recreating the table without the relationship. If you have tables with lots of columns and data, this process really becomes tedious.
However, SQLyog let you overcome this pain, and does all the steps internally. You are just required to select Delete. Internally, SQLyog does this using a 11-step process. If you want to delete an FK, just select the relationship from the Grid and press Delete.
Since, this process can result in loss of data SQLyog will ask for confirmation. Press Yes at your own risk.