Abstract: Associated with a canonical second order differential operator on frame bandles, there is a diffusion process.We denote by X={x∈C([0,1],Rd),x(x)=0},H=｛h∈X:‖h‖2H=∫10｜h··(t)｜2dt＜∞｝,Y=｛y∈C([0,1],s(d)):y(0)=0｝,K=｛k∈Y:‖k‖2K=∫10｜k·(t)｜2dt＜∞｝,then (β,ρ) is a Rd×s(d)-valued semimartingale satisfying the following SDE：dβ(t)=dh(t)+ρdx(t)-(dy(t))β,β(0)=0,dρ(t)=dk(t)+Ω(dx(t),β(t))+[ρ(t),dy(t)],ρ(0)=0.

Key words: diffusion process, ItO map, differential calculus