  Let $\mathfrak g$ be a Kac-Moody algebra. We show that every homogeneous
right coideal subalgebra $U$ of the multiparameter version of the quantized
universal enveloping algebra $U_q(\mathfrak{g}),$ $q^m\neq 1$ containing all
group-like elements has a triangular decomposition $U=U^-\otimes_{{\bf k}[F]}
{\bf k}[H] \otimes_{{\bf k}[G]} U^+$, where $U^-$ and $ U^+$ are right coideal
subalgebras of negative and positive quantum Borel subalgebras. However if $
U_1$ and $ U_2$ are arbitrary right coideal subalgebras of respectively
positive and negative quantum Borel subalgebras, then the triangular
composition $ U_2\otimes_{{\bf k}[F]} {\bf k}[H]\otimes_{{\bf k}[G]} U_1$ is a
right coideal but not necessary a subalgebra. Using a recent combinatorial
classification of right coideal subalgebras of the quantum Borel algebra
$U_q^+(\mathfrak{so}_{2n+1}),$ we find a necessary condition for the triangular
composition to be a right coideal subalgebra of $U_q(\mathfrak{so}_{2n+1}).$
  If $q$ has a finite multiplicative order $t>4,$ similar results remain valid
for homogeneous right coideal subalgebras of the multiparameter version of the
small Lusztig quantum groups $u_q({\frak g}),$ $u_q(\frak{so}_{2n+1}).$
