We study the decays B-c-->D* gamma and B-c-->D-s* gamma in the relativistic
independent quark model based on the confining potential in the scalar-vec
tor harmonic form. Out of the two competing mechanisms contributing to thes
e decays, we find that the weak annihilation contribution dominates the ele
ctromagnetic penguin one. Considering contributions from both mechanisms, t
otal decay widths and branching ratios are predicted as Gamma (B-c-->D* gam
ma) = 5.22X 10(-18) GeV, Gamma (B-c-->D-s* gamma) = 1.98X 10(-16) GeV and B
r(Bc-->D* gamma) similar or equal to 3.64X 10(-6) Br(B-c-->D-s* gamma) simi
lar or equal to 1.39X 10(-4) with tau (Bc) = 0.46 ps. The decays B-c-->D-s*
gamma can well be studied at CERN LHC in the near future.