  The tilt of bipolar magnetic region (BMR) is crucial in the Babcock--Leighton
process for the generation of the poloidal magnetic field in Sun. Based on the
thin flux tube model of the BMR formation, the tilt is believed to be caused by
the Coriolis force acting on the rising flux tube of the strong toroidal
magnetic field from the base of the convection zone (BCZ). We analyze the
magnetic field dependence of BMR tilts using the magnetograms of Michelson
Doppler Imager (MDI) (1996-2011) and Helioseismic and Magnetic Imager (HMI)
(2010-2018). We observe that the distribution of the maximum magnetic field
($B_{\rm max}$) of BMRs is bimodal. Its first peak at the low field corresponds
to BMRs which do not have sunspots as counterparts in the white light images,
whereas the second peak corresponds to sunspots as recorded in both types of
images. We find that the slope of Joy's law ($\gamma_0$) initially increases
slowly with the increase of $B_{\rm max}$. However, when $B_{\rm max} \gtrsim
2$ kG, $\gamma_0$ decreases. Scatter of BMR tilt around Joy's law
systematically decreases with the increase of $B_{\rm max}$. The decrease of
observed $\gamma_0$ with $B_{\rm max}$ provides a hint to a nonlinear tilt
quenching in the Babcock--Leighton process. We finally discuss how our results
may be used to make a connection with the thin flux tube model.
