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We propose an asymmetric photonic crystal (PC) waveguide, formed by moving the PC cladding on one side of the line defect along the waveguide core. By adjusting the structural parameters, we flatten the slow-mode dispersion curve, exclude the extreme points from the flat band, and avoid the unacceptably large dispersion induced by extreme points. We obtain an ultra-flat band with an inflection point corresponding to a slow-light mode with reduced distortion. We utilize the finite-difference time-domain method to verify the inflection-point ultraslow wave.