A new finite element discretization is presented for the low-order quasidiffusion (LOQD) equations, based on a linear-continuous finite elements (LCFE) discretization of a second-order form of the LOQD equations with the scalar flux as the only unknown. The high-order (transport) equation of the proposed QD method utilizes a standard linear-discontinuous finite element (LDFE) discretization [12] plus a hybrid-collocation Galerkin-S_N angular treatment [7]. The result is a completely finite element-based QD discretization. Numerical results demonstrate the expected first-order spatial convergence in a simple test and accuracy comparable to the pure LDFE transport discretization in a more complex one. Possible improvements to the method are discussed.