  Checking mesh validity is a mandatory step before doing any finite element
analysis. If checking the validity of tetrahedra is trivial, checking the
validity of hexahedral elements is far from being obvious. In this paper, a
method that robustly and efficiently compute the validity of standard linear
hexahedral elements is presented. This method is a significant improvement of a
previous work on the validity of curvilinear elements. The new implementation
is simple and computationally efficient. The key of the algorithm is still to
compute B\'ezier coefficients of the Jacobian determinant. We show that only 20
Jacobian determinants are necessary to compute the 27 B\'ezier coefficients.
Those 20 Jacobians can be efficiently computed by calculating the volume of 20
tetrahedra. The new implementation is able to check the validity of about 6
million hexahedra per second on one core of a personal computer. Through the
paper, all the necessary information is provided that allow to easily reproduce
the results, \ie write a simple code that takes the coordinates of 8 points as
input and outputs the validity of the hexahedron.
