Let
(
M
,
J
α
,
α
=
1
,
2
,
3
)
(M, J^\alpha , \alpha =1,2,3)
and
(
N
,
J
α
,
α
=
1
,
2
,
3
)
(N, \mathcal {J}^\alpha , \alpha =1,2,3)
be Hyperkähler manifolds. Suppose that
u
k
u_k
is a sequence of stationary quaternionic maps and converges weakly to
u
u
in
H
1
,
2
(
M
,
N
)
H^{1,2}(M,N)
, we derive a blow-up formula for
lim
k
→
∞
d
(
u
k
∗
J
α
)
\lim _{k\to \infty }d(u_k^*\mathcal {J}^\alpha )
, for
α
=
1
,
2
,
3
\alpha =1,2,3
, in the weak sense. As a corollary, we show that the maps constructed by Chen-Li [Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) 4 (2005), pp. 375–388] and by Foscolo [J. Differential Geom. 112 (2019), pp. 79–120] cannot be tangent maps (c.f Li and Tian [Internat. Math. Res. Notices 14 (1998), pp. 735–755], Theorem 3.1) of a stationary quaternionic map satisfing
d
(
u
∗
J
α
)
=
0
d(u^*\mathcal {J}^\alpha )=0
.