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The hybrid multi-bend achromat (HMBA) lattice concept is adopted in some diffraction-limited storage ring designs, which can permit relatively large on-momentum dynamic aperture and relatively weak sextupoles. In a typical HMBA lattice, the main arc section is constrained by the transverse phase advances making -I transformation for sextupole cancellation. In this paper, a new HMBA lattice concept with sextupole cancellation across straight section is proposed, where -I is made between adjacent dispersion bumps of two lattice cells. This makes the main arc section free of the phase advance constraint, and as a result, the number of bending magnets (bends) in the lattice cell and the cell tunes can be easily changed, thus providing more choices for lattice design. To achieve the large phase advances required for -I in this new concept, split bend is used as the matching bend, which is a bend split into two pieces with a quadrupole in between. The split bend also serves to reduce the emittance, and the large phase advances also give low beta functions in the straight section enhancing the insertion device brightness. Besides, for a given emittance goal, this new HMBA lattice can have less bends than the typical HMBA lattice due to stronger focusing in bend unit cells, which is beneficial for saving space and suppressing intra-beam scattering effect. Two lattices are given as examples to demonstrate this new concept and show its linear and nonlinear properties, and further extension is also discussed.