First, I would like to say that I have asked similar question to this before, but I noticed that many details are missing so I decided to rewrite the question with clear details.
I have a real matrix $D$ with size $m$ x $n$ , and $n < m$ such that $D'D = I_n$, where $D'$ denoted the transpose of the matrix $D$. I need to get the real matrix $V$ with size $n$ x $m$ such that $DV = Y$ where the matrix $Y$ has $Y'Y = I_m$ (It means get the matrix $V$ which make $(DV)'*(DV) = I_m)$. Does it exist? In other words it's to get the closest unitary matrix $Y$ by non-square matrix $V$.
In case if the matrix $V$ is square, I think the solution can be straightforward, but what's about it's not square? let's take an example that $m$=6 and $n$=4.