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Whilst Snapchat is intended to be a secure method of communication of pictures, its not really designed that way. Once a user has downloaded an image it is possible to save it through screen capture or an alternative application such as a Snapchat PC app.
In truth, Snapchat isn't that secure.
It’s possible using a rooted android device. Android = creeper friendly! http://galaxy-note2.wonderhowto.com/how-to/save-snapchats-secretly-onto-...