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Let IE be a complete ultrametric space, let IK be a perfect complete ultrametric field and let A be a Banach IK-algebra which is either a full IK-subalgebra of the algebra of continuous functions from IE to IK owning all characteristic functions of clopens of IE, or a full IK-subalgebra of the algebra of uniformly continuous functions from IE to IK owning all characteristic functions of uniformly open subsets of IE. We prove that all maximal ideals of finite codimension of A are of codimension

Finite codimensional maximal ideals in subalgebras of ultrametric uniformly continuous functions