It is of great significance to clarify the influence of transverse magnetic field (TMF) on arc control in high-voltage direct current (HVDC) relays. In this paper, the influence of TMF in a wide range of 0–140 mT on the arc characteristics of HVDC relays is studied, the experimental observations of arc reignition are carried out and the effect of arc reignition on contact erosion, the criterion of arc reignition and the mechanism of TMF enhancement on arc reignition are further analyzed. The results show that the TMF enhancement is beneficial for shortening the arc voltage stagnation duration and accelerating the speed of arc elongation, arc dispersion and dispersed arc motion, thereby improving the arc extinguishing performance. However, higher TMF leads to more severe and earlier arc reignition, as also shown in the experimental observations. The arc reignition further causes a sudden drop in arc voltage, prolonged arc duration and uneven contact erosion. To evaluate the occurrence of arc reignition caused by TMF enhancement, a simplified breakdown criterion is proposed through the defined characteristic variable
C
¯
(
t
)
. Based on this, the mechanism by which the TMF enhancement more easily causes arc reignition is explained, that is the higher TMF leads to an earlier and faster increase in
C
¯
(
t
)
and slightly reduces the breakdown threshold
C
¯
∗
(
t
5
,
D
)
. Further, measures to suppress the arc reignition are proposed.