Frances, If you're using OS X...
1. Go to System Preferences>Accounts.
2. Select the Login Items (or Startup Items) Pane.
3. In the next window, select/highlight Safari. I'm presuming it's there. If it is, that is why Safari is launching upon startup.
4. Click on the "-" button below the list (not the "-" sign below the Login Options). That will delete Safari from the startup list.
5. Close System Preferences.
Note: You may need to first click on/open the lock in order to make the change.
HTH