A local Jordan algebra J \mathfrak {J} is a unital quadratic Jordan algebra in which Rad ⁡ J \operatorname {Rad} \mathfrak {J} is a maximal ideal, J / Rad ⁡ J \mathfrak {J}/\operatorname {Rad} \mathfrak {J} satisfies the DCC, and ∩ k Rad ⁡ J ( k ) = 0 { \cap _k}\operatorname {Rad} {\mathfrak {J}^{(k)}} = 0 where K ( n + 1 ) = U K ( n ) K ( n ) {K^{(n + 1)}} = {U_K}(n){K^{(n)}} . We show that the completion of a local Jordan algebra is also local Jordan, and if J \mathfrak {J} is a complete local Jordan algebra over a field of characteristic not 2, then either (1) J \mathfrak {J} is a complete completely primary Jordan algebra, (2) J ≅ J 1 ⊕ J 2 ⊕ S \mathfrak {J} \cong {\mathfrak {J}_1} \oplus {\mathfrak {J}_2} \oplus S where each J i {\mathfrak {J}_i} is a completely primary local Jordan algebra, or (3) J ≅ H ( D n , J a ) \mathfrak {J} \cong \mathfrak {H}({D_n},{J_a}) where ( D , j ) (D,j) is either a not associative alternative algebra with involution or a complete semilocal associative algebra with involution.