Modification of the lattice Boltzmann method for computation of viscous incompressible fluid flows is proposed.The method is based on the splitting of differential operator in Navier - Stokes equation and on the idea ofinstantaneous Maxwellisation of distribution function. The method is based on explicit schemes and didn'thave any problems with parallelization of computations. The stability of the method is demonstrated usingvon Neumann method in a wide range of input parameter values. The efficiency of the method proposed isdemonstrated on the solution of the problem on the planar cavity flow.