In this paper, we build and analyze the stability of a collocated scheme, involving a specific numerical diffusion operator, for the isentropic Euler equations. This scheme is based on the numerical diffusion operator of a family of staggered finite volume schemes introduced in [1]. The properties of this operator allowed to understand the L 2-stability of staggered finite volume methods. Staggered schemes are popular in the thermal hydraulics community for their reported robustness and lack of spurious oscillations. The contributions of this paper are twofold: we firstly build a colocated scheme with a staggered-based numerical diffusion operator, hence the proposed terminology of "pseudo-staggered" scheme, and we secondly present a rigorous TVD analysis, in order to explain the non-oscillatory behaviour of staggered discretisations.