A simple estimation of the absolute value of the error in the dependence of the step number performed for the implicit (backward) Euler method has been derived for the case of a single ordinary differential equation (ODE). This estimation distinctly shows the way and the degree to which the implicit Euler method (recommended in user guides for the RELAP4 family of codes) can give more inaccurate results than the explicit (forward) method. The short and simple reasoning presented should be treated as an indication of the problem. Error estimation for a general system of ODEs is an extremely difficult and complex task, and it is still not completely solved.