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A $26 \times 26$ square divides into different rectangles so that each occurs exactly twice in different orientations.

twice used rectangles

I've also found a solution for the $10 \times 10$ square, but no others. Are there any other squares that can be divided into a finite number of rectangles so that each occurs exactly twice in different orientations?

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    Do you mean that you have ruled it out for squares of length less than 26, unequal to 10? – 2017-01-17
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    I haven't ruled out anything yet. My solving programs are geared for the [Mondrian Art Problem](http://demonstrations.wolfram.com/MondrianArtProblem/) at the moment, and I need to loosen some parameters to be sure about anything on this one. – 2017-01-17

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Let us consider the following tiling of $8 \times 8$ square: 11111222 11111222 11111222 55557222 64497222 64493333 64493333 64400088 Each digit indicates number of rectangle the cell belongs to. From 0 to 9 the sizes are: $3 \times 1$, $3 \times 5$, $5 \times 3$, $4 \times 2$, $2 \times 4$, $4 \times 1$, $1 \times 4$, $1 \times 2$, $2 \times 1$, $1 \times 3$.