Are the two examples of $4\times 4$ anti-magic squares currently on Wikipedia actually anti-magic squares under the definition given there?
The examples are:
$\left[ \begin {array}{cccc} 2&15&5&13\\16&3&7&12\\ 9&8&14&1\\ 6&4&11&10 \end {array} \right]$
and $\left[ \begin {array}{cccc} 1&13&3&12\\15&9&4&10\\ 7&2&16&8\\ 14&6&11&5 \end {array} \right]$