diff --git a/src/Functions/negate.cpp b/src/Functions/negate.cpp
index 2c9b461274d..91e64e98c6b 100644
--- a/src/Functions/negate.cpp
+++ b/src/Functions/negate.cpp
@@ -32,9 +32,48 @@ using FunctionNegate = FunctionUnaryArithmetic<NegateImpl, NameNegate, true>;
 template <> struct FunctionUnaryArithmeticMonotonicity<NameNegate>
 {
     static bool has() { return true; }
-    static IFunction::Monotonicity get(const Field &, const Field &)
+    static IFunction::Monotonicity get(const Field & left, const Field & right)
     {
-        return { .is_monotonic = true, .is_positive = false, .is_strict = true };
+        /// negate(UInt64) -> Int64:
+        ///  * monotonically decreases on [0, 2^63] (no overflow),
+        ///  * then jumps up from -2^63 to 2^63-1, then
+        ///  * monotonically decreases on [2^63+1, 2^64-1] (with overflow).
+        /// Similarly for UInt128 and UInt256.
+        /// Note: we currently don't handle the corner case -UINT64_MIN == UINT64_MIN, and similar for floats and wide signed ints.
+        /// (This implementation seems overcomplicated and not very correct, maybe there's a better way to do it,
+        ///  maybe by using the actual IDataType instead of two field types.)
+
+        /// We don't know the data type, assume nonmonotonic.
+        if (left.isNull() && right.isNull())
+            return { .is_monotonic = false, .is_positive = false, .is_strict = true };
+
+        auto which_half_if_unsigned_or_infinity = [](const Field & f, int half_if_null, bool & is_unsigned) -> int
+        {
+            is_unsigned = true;
+            switch (f.getType())
+            {
+                case Field::Types::UInt64: return (f.safeGet<UInt64>() > 1ul << 63) ? +1 : -1;
+                case Field::Types::UInt128: return (f.safeGet<UInt128>() > UInt128(1) << 127) ? +1 : -1;
+                case Field::Types::UInt256: return (f.safeGet<UInt256>() > UInt256(1) << 255) ? +1 : -1;
+                default: break;
+            }
+            is_unsigned = false;
+            if (f.isPositiveInfinity())
+                return +1;
+            if (f.isNegativeInfinity())
+                return -1;
+            if (f.isNull())
+                return half_if_null;
+            return 0;
+        };
+        bool left_is_unsigned, right_is_unsigned;
+        int left_half = which_half_if_unsigned_or_infinity(left, -1, left_is_unsigned);
+        int right_half = which_half_if_unsigned_or_infinity(right, +1, right_is_unsigned);
+
+        bool is_monotonic = true;
+        if (left_is_unsigned || right_is_unsigned)
+            is_monotonic = left_half * right_half >= 0; /// either both values in the same half or unexpected signed-unsigned mix
+        return { .is_monotonic = is_monotonic, .is_positive = false, .is_strict = true };
     }
 };
 
diff --git a/tests/queries/0_stateless/03259_negate_key_overflow.reference b/tests/queries/0_stateless/03259_negate_key_overflow.reference
new file mode 100644
index 00000000000..bda709ecfb4
--- /dev/null
+++ b/tests/queries/0_stateless/03259_negate_key_overflow.reference
@@ -0,0 +1,3 @@
+42
+42
+42
diff --git a/tests/queries/0_stateless/03259_negate_key_overflow.sql b/tests/queries/0_stateless/03259_negate_key_overflow.sql
new file mode 100644
index 00000000000..eb825615e74
--- /dev/null
+++ b/tests/queries/0_stateless/03259_negate_key_overflow.sql
@@ -0,0 +1,14 @@
+create table a (x UInt64) engine MergeTree order by x;
+insert into a values (12345678901234567890), (42);
+select * from a where -x = -42;
+drop table a;
+
+create table a (x UInt128) engine MergeTree order by x;
+insert into a values (170141183460469231731687303715884105828), (42);
+select * from a where -x = -42;
+drop table a;
+
+create table a (x UInt256) engine MergeTree order by x;
+insert into a values (57896044618658097711785492504343953926634992332820282019728792003956564820068), (42);
+select * from a where -x = -42;
+drop table a;