In this paper, we show that by sending the normal stabilization function to infinity in the hybridizable discontinuous Galerkin methods previously proposed in [Comput. Methods Appl. Mech. Engrg. 199 (2010), 582–597], for Stokes flows, a new class of divergence-conforming methods is obtained which maintains the convergence properties of the original methods. Thus, all the components of the approximate solution, which use polynomial spaces of degree
k
k
, converge with the optimal order of
k
+
1
k+1
in
L
2
L^2
for any
k
≥
0
k \ge 0
. Moreover, the postprocessed velocity approximation is also divergence-conforming, exactly divergence-free and converges with order
k
+
2
k+2
for
k
≥
1
k\ge 1
and with order
1
1
for
k
=
0
k=0
. The novelty of the analysis is that it proceeds by taking the limit when the normal stabilization goes to infinity in the error estimates recently obtained in [Math. Comp., 80 (2011) 723–760].