diff --git a/src/core/MOM_dynamics_split_RK2.F90 b/src/core/MOM_dynamics_split_RK2.F90
index 8588a0c41e..62182a4cbb 100644
--- a/src/core/MOM_dynamics_split_RK2.F90
+++ b/src/core/MOM_dynamics_split_RK2.F90
@@ -60,6 +60,8 @@ module MOM_dynamics_split_RK2
 use MOM_lateral_mixing_coeffs, only : VarMix_CS
 use MOM_MEKE_types,            only : MEKE_type
 use MOM_open_boundary,         only : ocean_OBC_type, radiation_open_bdry_conds
+use MOM_open_boundary,         only : OBC_segment_type, OBC_DIRECTION_E, OBC_DIRECTION_W
+use MOM_open_boundary,         only : OBC_DIRECTION_N, OBC_DIRECTION_S
 use MOM_open_boundary,         only : open_boundary_zero_normal_flow, open_boundary_query
 use MOM_open_boundary,         only : open_boundary_test_extern_h, update_OBC_ramp
 use MOM_open_boundary,         only : copy_thickness_reservoirs
@@ -419,6 +421,8 @@ subroutine step_MOM_dyn_split_RK2(u_inst, v_inst, h, tv, visc, Time_local, dt, f
   integer :: i, j, k, is, ie, js, je, Isq, Ieq, Jsq, Jeq, nz
   integer :: cont_stencil, obc_stencil, vel_stencil
   integer :: cor_stencil
+  integer :: n                                         ! OBC segment loop index (OBC-exterior h fix)
+  type(OBC_segment_type), pointer :: segment => NULL() ! OBC segment (OBC-exterior h fix)
 
   is  = G%isc  ; ie  = G%iec  ; js  = G%jsc  ; je  = G%jec ; nz = GV%ke
   Isq = G%IscB ; Ieq = G%IecB ; Jsq = G%JscB ; Jeq = G%JecB
@@ -465,6 +469,39 @@ subroutine step_MOM_dyn_split_RK2(u_inst, v_inst, h, tv, visc, Time_local, dt, f
     ! Update OBC ramp value as function of time
     call update_OBC_ramp(Time_local, CS%OBC, US)
 
+    ! === OBC-exterior h fix (minimal): the OBC-exterior h halo is not reconstructed
+    ! bit-for-bit across an exact restart, and vertvisc_coef reads it (zero-gradient
+    ! projection across OBCs), seeding a last-bit velocity divergence. Rebuild it here with a
+    ! single in-place zero-gradient fill over all segments: copy the first interior thickness
+    ! into the exterior ghost cell. u-points (E/W) and v-points (N/S) only read same-row /
+    ! same-column neighbours, never the diagonal corner, so no corner handling is needed.
+    if (associated(CS%OBC)) then
+      do n=1,CS%OBC%number_of_segments
+        segment => CS%OBC%segment(n)
+        if (.not. segment%on_pe) cycle
+        if (segment%is_E_or_W) then
+          I = segment%HI%IsdB
+          do k=1,nz ; do j=segment%HI%jsd,segment%HI%jed
+            if (segment%direction == OBC_DIRECTION_W) then
+              h(I,j,k)   = h(I+1,j,k)
+            elseif (segment%direction == OBC_DIRECTION_E) then
+              h(I+1,j,k) = h(I,j,k)
+            endif
+          enddo ; enddo
+        elseif (segment%is_N_or_S) then
+          J = segment%HI%JsdB
+          do k=1,nz ; do i=segment%HI%isd,segment%HI%ied
+            if (segment%direction == OBC_DIRECTION_S) then
+              h(i,J,k)   = h(i,J+1,k)
+            elseif (segment%direction == OBC_DIRECTION_N) then
+              h(i,J+1,k) = h(i,J,k)
+            endif
+          enddo ; enddo
+        endif
+      enddo
+    endif
+    ! === end OBC-exterior h fix ===
+
     do k=1,nz ; do j=G%jsd,G%jed ; do I=G%IsdB,G%IedB
       u_old_rad_OBC(I,j,k) = u_av(I,j,k)
     enddo ; enddo ; enddo