The Haar wavelet decomposition technique is used to detect the planetary magnetosphere boundaries and discontinuities. We use the magnetometer data from the CASSINI and MESSENGER spacecraft to identify the abrupt changes in the magnetic field when the spacecraft crossed the magnetospheric bow shocks and magnetopauses of Saturn and Mercury, respectively. The results confirm that the Haar transform can efficiently identify the planetary magnetosphere boundaries characterized by the abrupt magnetic field changes. It is suggested that this technique can be applied to detect the planetary boundaries as well as the discontinuities such as the shock waves in the interplanetary space.