Theoretical time step constraints of semi-implicit schemes are known to be more
 restrictive than should be in practice. We intend to alleviate the constraints with more
 smoothness assumptions on the solutions. By introducing a new scheme with modification on the treatment of the nonlinear term, we are able to prove that the scheme
 is unconditionally stable and convergent. Further more, we show that the modified
 scheme and the original semi-implicit one are equivalent under a weak condition on the
 time step and the number of space discretion points.