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#J, <strike>31</strike> <strike>30</strike> <strike>14</strike> <strike>12</strike> 11 bytes

 [:;<@|.`</.

<strike>[Ych][1]. Too big.</strike>

Takes a matrix as input.

**Explanation**

J has an advantage here. There's a command called [oblique][2] (`/.`) which takes the oblique lines in turn and applies a verb to them. In this case I'm using a gerund to apply two verbs alternately: `<` ([box][3]) and `<@|.` ([reverse][4] and box). Then it's just a matter of unboxing everything using `;` ([raze][5]).


 [1]: https://en.wiktionary.org/wiki/ych_a_fi
 [2]: http://jsoftware.com/help/dictionary/d421.htm
 [3]: http://jsoftware.com/help/dictionary/d010.htm
 [4]: http://jsoftware.com/help/dictionary/d231.htm
 [5]: http://jsoftware.com/help/dictionary/d330.htm