Not In all flight, it changes trajectories according to the guidance and terrain
FLIGHT TRAJECTORY
The flight path followed by cruise missiles depends on their launch platform, guidance systems, and the target.
- Sea skimming / Terrain Hugging
Anti-ship cruise missiles generally follow a sea skimming profile. This means that the missile flies just a few meters above the water surface. This flight profile makes the missile invisible to enemy radar until it is just round 30 km away from the ship due to the earth’s curvature. Flying low delays its detection by the enemy unless the enemy has an airborne radar. But flying low has its disadvantages as well. Fuel consumption is high when following a sea skimming profile. Range at sea skimming height is 30-40% of the range at high attitude flight.
Land attack missiles generally follow a terrain hugging profile. This means that they closely follow the ups and downs of the terrain and remain hidden from detection by radars due to their low altitude.
BRAHMOS USES
Mixed altitude profile
Many cruise missiles follow a mixed trajectory. Once they are launched, they fly at high altitudes for optimum range and when they approach their target, they climb down to a few meters altitude and make their final approach towards the target. This offers the range advantage of high altitude flight and the radar-evading ability of the sea-skimming flight. Many modern cruise missiles follow this flight profile and some of them go supersonic at the terminal sea skimming phase.
UNLIKE OTHER SUPERSONIC CRUISE BRAHMOS FLY SUPERSONIC THROUGHOUT ITS ALL FLIGHT
https://defencyclopedia.com/2014/08/01/explained-how-cruise-missiles-work/