Remove the squares

There are forty matches in a grid pattern as shown above.  Try to remove matches so that no squares remain.  That means no 1x1 squares, no 2x2 squares, no 3x3 squares, and 4x4 squares.

Here's one solution: remove all vertical matches.  No squares are left.  I needed to remove twenty matches.  Can you do better?

I labeled each match with a number so that you can describe your solution easily.

See the solution