QR decomposition, completing Q

Potentially stupid question but bear with me...

So, after QR factorization [after Gram-Schmidt and defining R], we got an mxn-matrix A that is equal an mxn-matrix Q times an nxn-matrix R

A = QR

Now, script states "we may now** complete the n orthonormal Vectors q1,...,qn **[which, by the way, are the columns of Q] **to an orthonormal basis of E^m** [E being either the real or the complex numbers]"

So ... how do I do that?

**Do I simply take ***any* linearly independent m-vectors and add it to Q or need I calculate the missing m-n vectors and if the latter, how?

Note: It might be conducive to know that after completing Q to an mxm-matrix Q' we add m-n 0-row-vectors to R (becoming an mxn-matrix R') so as to get what the author of the scipt calls the actual QR decomposition:

A = Q'R'

Any help appreciated