Throughout this paper, we use the following notations: Let v = v ( p ) satisfy (1.1)–(1.3). We discuss the following coefficient inverse problem. Problem 1 Determine the coefficient p ( x, y ) , ( x, y ) ∈ D × G in (1.1)–(1.3) by the extra data ∂$_{ν}$ v ( p ) | $_{Σ}$, where ν ∈ R n denotes the unit outward normal vector to ∂D and ∂$_{ν}$ v = ∇ v · ν is the normal derivative. Ultrahyperbolic Schr¨ odinger equations arise in several applications, for example in water wave problems, [10, 11, 14, 34, 35] and in higher dimensions as com- pletely integrable models, see [1, 25]. There have been limited number of studies on the direct problems for these equations. The local well posedness of the initial value problem was investigated in [19-21]. To our best knowledge there is no result available in the mathematical literature related to the inverse problems for ultra- hyperbolic Schr¨ odinger equations. In this work, we obtain a Carleman estimate and prove conditional H¨ older stability for the inverse problem of determining a coefficient or a source term in ultrahyperbolic Schr¨ odinger equation. T. Carleman [8] established the first Carleman estimate in 1939 for proving the unique continuation for a two-dimensional elliptic equation. In 1954, C. M¨ uller extended Carleman’s result to R $^{n}$, [18]. After that A. P. Calder´ on [7] and L. H¨ ormander [13] improved these results based on the concept of pseudo-convexity. In the theory of inverse problems, Carleman estimates were firstly introduced by A. L. Bukgeim and M. V. Klibanov in [6]. After that, there have been many works relying on that method with modified arguments. Puel and Yamamoto [28], Isakov and Yamamoto [17], Imanuvilov and Yamamoto [15, 16], Bellassoued and Yamamoto [5], Klibanov and Yamamoto [24] have obtained various stability esti- mates for inverse problems for hyperbolic equation. We refer to Yamamoto [31] for a comprehensive survey about the stability and 2 ∂$_{t}$ = ∂ ∂t , ∂$_{x}$$_{i}$ = ∂ ∂x$_{i}$ , ∂$_{y}$$_{j}$ = ∂ ∂y$_{j}$ , ∇ x = ( ∂$_{x}$$_{1}$ , ∂$_{x}$$_{2}$ , ..., ∂$_{x}$$_{n}$ ) , ∇ y = ( ∂$_{y}$$_{1}$ , ∂$_{y}$$_{2}$ , ..., ∂$_{y}$$_{m}$ ) , Δ$_{x}$ = ∑ i =1 ∂ 2 $_{x$_{i}$}$, Δ$_{y}$ = ∑ j =1 ∂ 2 $_{y$_{j}$}$.