Abstract: In the paper, we introduce weak Bessel sequences and weak frames in a Hilbert C*-module H, and give a characterization of weak Bessel sequences, weak frames, normalized tight weak frames, and dual weak frames to each other, respectively. Using A-valued linear bounded operator U:H → l²(A), V*U = I, a coustructing method of dual weak frame {x*_j: j ∈ J} for a given weak frame {x_j: j ∈ J} is obtained. Moreover, pseudo frame decompositions for H is given.

Key words: C*-algebra, Hilbert C*-module frame, dual frame, frame decomposition