Truly secure backup method for Mac laptop to external hard drive

Hi all, I am looking for a secure way to backup my MacBook running either Mavericks or Yosemite, preferably Yosemite.  Can I use File Vault to encrypt my laptop data and then use Time Machine to securely backup to an external hard drive?  Does the hard drive need to be encrypted as well?  I am in a situation where my backup drive would be exposed to theft at times and want to make sure that even if stolen, no one could obtain the data on the drive from the Time Machine backups.  Please tell me what I need and how to do it.  Thank you very much.
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You can set TimeMachine to encrypt your backups. See:

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so... have you tried Carbon Copy Cloner yet?
mjchevalierAuthor Commented:
Thank you sunnysinghlee, I did look at the link you attached. While the feature list is impressive, I did not see anything regarding the security or encryption of backups?
Sorry! I am brand new user.
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