Robust observer design is developed for a normal form system with a prescribed upper bound on the observer convergence time irrespective of initial state values and matched uniformly bounded disturbances. The design recasts a finite-time observer, especially developed for a system composed of diagonal and over-diagonal forms, and it is based on the scaling technique. The proposed observer operates with time-varying gains, uniformly bounded on an infinite horizon, thereby yielding an attractive implementation opportunity compared to the original design by Holloway and Krstic [6] with time-varying gains, which escape to infinity as time goes to the prescribed time instant. Capabilities of the present observer are supported in a numerical study, performed for a perturbed triple integrator, and are compared to existing prescribed-time and fixed-time observers.