<p>We propose a new deterministic block Kaczmarz-type method for solving large-scale consistent systems of linear equations. In the proposed method, the block of the subsystem of linear equations is determined by an easier to compute method, and it is pseudoinverse-free to solve the subsystem. To further accelerate the convergence rate of the proposed method, we present an accelerated version of this method using momentum. Linear convergence of the proposed method and its acceleration are proved. Numerical results show that the proposed method and its acceleration are effective and very fast for the test problems.</p>