diff --git a/thue-morse.v b/thue-morse.v
index a2c625d..8e84ab3 100644
--- a/thue-morse.v
+++ b/thue-morse.v
@@ -846,12 +846,13 @@ Require Import BinPosDef.
 
 
 (* Autre construction de la suite, ici n est le nombre de termes *)
-Fixpoint tm_bin (n: nat) : list bool :=
+(* la construction se fait à l'envers *)
+Fixpoint tm_bin_rev (n: nat) : list bool :=
   match n with
   | 0 => nil
-  | S n' => let t := tm_bin n' in
+  | S n' => let t := tm_bin_rev n' in
             let m := Pos.of_nat n' in
-              (xorb (hd false t)
+              (xorb (hd true t)
                 (odd (Pos.size_nat
          match Pos.lxor m (Pos.pred m) with
          | N0 => BinNums.xH
@@ -859,6 +860,21 @@ Fixpoint tm_bin (n: nat) : list bool :=
          end))) :: t
   end.
 
+Fixpoint tm_bin (n: nat) : list bool :=
+  match n with
+  | 0 => nil
+  | S n' => let t := tm_bin n' in
+            let m := Pos.of_nat n' in
+            t ++ [ xorb (last t true)
+                (odd (Pos.size_nat
+         match Pos.lxor m (Pos.pred m) with
+         | N0 => BinNums.xH
+         | Npos(p)  => p
+         end)) ]
+  end.
+
+Compute tm_bin 16 = tm_step 4.
+
 
 Theorem tm_step_consecutive : forall (n : nat) (l1 l2 : list bool) (b1 b2 : bool),
   tm_step n = l1 ++ b1 :: b2 :: l2 ->