Why is the maximum value of an orthonormal dictionary of size $N \times N$ less than that of another having size $M \times M$, where M>N?

Question

I was trying to compare the maximum value in DCT dictionary (representing an orthonormal dictionary) of size $N \times N$ to that of another DCT dictionary of size $M \times M$, where $M>N$. I always found that the highest value of $DCT_{M \times M} > DCT_{N \times N}$? Is there any mathematical reason behind it? Can this be generalized for all orthonormal dictionaries?