It is indeed possible. If the teams are labelled A to L, and the dashed lines separate the weeks, then I think this schedule will work:
(A B) (D F) (K L)
(E H) (I J) (C G)
(B K) (A D) (F L)
(C E) (G I) (H J)
------------------
(E F) (A K) (B I)
(G L) (D J) (C H)
(B F) (E K) (A I)
(C D) (H L) (G J)
------------------
(G K) (B C) (F J)
(A L) (H I) (D E)
(B G) (C J) (F K)
(A H) (D L) (E I)
------------------
(C I) (F H) (D K)
(B J) (A G) (E L)
(C F) (I K) (D H)
(E G) (B L) (A J)
------------------
(C K) (G H) (A F)
(B E) (J L) (D I)
(F G) (A C) (H K)
(B D) (E J) (I L)
------------------
(F I) (C L) (J K)
(A E) (B H) (D G)