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We develop a simple and effective method for solving the Schrödinger equation of a hydrogen atom in a constant magnetic field with arbitrary strength. Energies are obtained not only for the ground and low-lying states but also for highly excited states with precision from 12 up to 20 decimal digits. The calculations are performed for an entire range of magnetic field intensity up to 9. 4 × 1 0 8 Tesla, the strongest field ever observed. The strong point of the development of the method is the construction of an anharmonic oscillator model for a hydrogen atom in a constant magnetic field via the Kustaanheimo–Stiefel transformation. This model allows the use of purely algebraic calculations and the Feranchuk–Komarov (FK) operator method for effectively solving the Schrödinger equation. The advantages of the basis set in this work are also discussed to extend its application to other problems, such as multi-electron atoms in a constant magnetic field. We also provide a program written by FORTRAN for the solutions mentioned above. Program Title: CHAMF Program Files doi: http://dx.doi.org/10.17632/s5shscgfcj.1 Licensing provisions: BSD 3-clause Programming language: FORTRAN77 Nature of problem: The Schrödinger equation for a hydrogen atom in a magnetic field is rewritten into that of a four-dimensional anharmonic oscillator by using the Kustaanheimo–Stiefel transformation. The later has a structure more convenient for applying the algebraic method based on annihilation and creation operators. Therefore, the FK operator method [1] can be applied for obtaining high-accuracy numerical solutions which means the obtained energies converge to a given precision (up to twenty decimal digits in this work). The method is developed for an entire range of magnetic field intensity up to 9. 4 × 1 0 8 Tesla and for not only ground state but also highly excited states. Solution method: The FK operator method is modified and used for the high-accuracy numerical solutions. This method combines with the algebraic technique which is useful for calculating all the needed matrix elements. Thus, the Schrödinger equation becomes the symmetric generalized eigenvalue problem which can be solved by the subroutine dsygvx.f of the LAPACK library [2]. For the better accuracy with quadruple precision, we modify this subroutine and its dependence with using the real*16 number instead of the real*8. Moreover, a free parameter introduced by the FK operator method can be used for increasing the speed of convergence. The optimal choice of this free parameter is implemented in the program. Additional comments including restrictions and unusual features: Operating system: Linux. RAM: at least 1 GByte per core. The gfortran compiler is recommended for this program. The running time is from a centisecond to a few minutes depending on the required precision. However, for the super-strong magnetic fields (γ ≥ 200), the running time may reach to two hours for the precision of twelve decimal digits, and RAM is needed to be at least 60 GB. [1] I. Feranchuk, A. Ivanov, Van-Hoang Le, A. Ulyanenkov, Non-perturbative Description of Quantum Systems, Springer, Switzerland, 2015. doi:10.1007/978-3-319-13006-4. [2] Netlib.org. LAPACK: Linear Algebra PACKage, Subroutine dsygvx.f. URL http://www.netlib.org/lapack/lapack-3.1.1/html/dsygvx.f.html [ABSTRACT FROM AUTHOR]