  We consider the discretization effects of a string-bit model simulating the
near-BMN operators in the super--Yang--Mills model. The fermionic sector of
this model is altered by the so called species doubling. We analyze the
possibilities to cure this disease and propose an alternative formulation of
the fermionic sector free from the above drawbacks. Also we propose a
formulation of string bits with exact supersymmetry, which produces however an
even number of continuous strings in the limit $J\to\infty$.
