In the very nice paper by GW Stewart:
Stewart, G. W., The efficient generation of random orthogonal matrices with an application to condition estimators. (With mircofiche section), SIAM J. Numer. Anal. 17, 403-409 (1980). ZBL0443.65027.
The author gives the following algorithm for generating a Haar-uniform orthogonal matrix: Let $M$ be an $n\times n$ matrix with i.i.d gaussian entries. Let $M= QR$ be the $QR$ decomposition of $M$ ($Q$ is orthogonal, $R$ is upper-triangular, with positive diagonal entries). Then $Q$ is Haar-uniform.
My question is: What is the distribution of $R?$