The physical and orbital parameters of the quadruple star system ι UMa (HD 76644 = ADS 7114) were determined earlier, when it was concluded based on modeling the system's dynamics and applying theoretical stability criteria that the system was probably unstable. Here the stability of the ι UMa system is studied by calculating the Lyapunov characteristic exponents for representative sets of parameters and initial conditions. The conclusions on the system's stability (or instability) based on various stability criteria and the calculated Lyapunov exponents are compared. The instability of the system as a whole is confirmed rigorously based on massive computations of the Lyapunov exponents. This system appears to be the only known multiple system whose instability has been rigorously established. The Lyapunov time-disruption time statistical relations are constructed, which show that the Hamiltonian intermittency of the second kind dominates. Typical disruption times are shorter than 1000 years, and the Lyapunov times are shorter than 100 years.