Bounds for the error of the Gaussian approximation for the binomial distribution are stated, depending from the probability of success and the number  n of observations. As a consequence, the upper  bound for the absolute constant in the Berry--Esseen inequality for identically distributed random variables, taking two values, is deduced which differs from asymptotical one slightly more than 0.01. 
     The following idea is realized in the work. We can obtain   sharp bounds for sufficiently large n. The main purpose of the paper is to prove just these bounds. As to bounded number  of observations,
computations with the help of the computer must be produced. This part of investigations is developed by our pupils K.V. Mikhailov and A.S. Kondric.