If the condition number of a matrix is minimized then the matrix is orthogonalized?

Question

I know that if a square matrix is orthogonal, then its condition number is 1. I was wondering if the converse is true ? I have a non-square structured matrix and I want that the matrix be orthogonal by rows. In order to construct an orthogonal matrix, preserving its structure, I propose an optimization problem which minimizes the condition number. I achieve good results, however I don't known if by minimizing the condition number I always obtain an orthogonal matrix ( orthogonal by rows). My assumption is correct ? Thank you.