[Haskell-beginners] Built-in/more elegant version of this function?

[Jordan Cooper]

I was wondering if there is a built-in way to do what this function I
wrote does (or at least a more elegant way, preferably without
explicit recursion).

f xss = map safeHead xss : f (map safeTail xss)

(where safeHead/Tail are versions of head/tail that don't crash on [] input)