diff --git a/include/xsf/cephes/ellpj.h b/include/xsf/cephes/ellpj.h
index 7221b7b923..06845e832f 100644
--- a/include/xsf/cephes/ellpj.h
+++ b/include/xsf/cephes/ellpj.h
@@ -82,7 +82,7 @@ namespace cephes {
         int i;
 
         /* Check for special cases */
-        if (m < 0.0 || m > 1.0 || std::isnan(m)) {
+        if (m > 1.0 || std::isnan(m)) {
             set_error("ellpj", SF_ERROR_DOMAIN, NULL);
             *sn = std::numeric_limits<double>::quiet_NaN();
             *cn = std::numeric_limits<double>::quiet_NaN();
@@ -90,6 +90,22 @@ namespace cephes {
             *dn = std::numeric_limits<double>::quiet_NaN();
             return (-1);
         }
+        /* Handle negative m by transformation (DLMF 22.17) */
+        if (m < 0.0) {
+            double m1 = -m / (1.0 - m);
+            double u1 = std::sqrt(1.0 - m) * u;
+            double sn_p, cn_p, dn_p, ph_p;
+
+            int result = ellpj(u1, m1, &sn_p, &cn_p, &dn_p, &ph_p);
+            if (result != 0)
+                return result;
+
+            *sn = sn_p / (std::sqrt(1.0 - m) * dn_p);
+            *cn = cn_p / dn_p;
+            *dn = 1.0 / dn_p;
+            *ph = std::atan2(*sn, *cn);
+            return (0);
+        }
         if (m < 1.0e-9) {
             t = std::sin(u);
             b = std::cos(u);
diff --git a/tests/xsf_tests/test_ellpj.cpp b/tests/xsf_tests/test_ellpj.cpp
new file mode 100644
index 0000000000..41282c76ff
--- /dev/null
+++ b/tests/xsf_tests/test_ellpj.cpp
@@ -0,0 +1,67 @@
+#include "../testing_utils.h"
+#include <iostream>
+#include <tuple>
+#include <xsf/cephes/ellpj.h>
+
+TEST_CASE("ellpj negative m", "[ellpj][xsf_tests]") {
+    // u_values = [-10, -6, -2, 2, 6, 10]
+    // Reference values computed with mpmath
+
+    using test_case = std::tuple<double, double, double, double, double>;
+    // u, m, ref_sn, ref_cn, ref_dn
+
+    auto [u, m, ref_sn, ref_cn, ref_dn] = GENERATE(
+        // m = -2
+        test_case{-10.0, -2.0, -0.649677834014239, 0.760209650024628, 1.3579994757064},
+        test_case{-6.0, -2.0, -0.969931206391936, -0.243379240830198, 1.69750790580363},
+        test_case{-2.0, -2.0, -0.348621324159513, -0.937263662125694, 1.11493213036376},
+        test_case{2.0, -2.0, 0.348621324159513, -0.937263662125694, 1.11493213036376},
+        test_case{6.0, -2.0, 0.969931206391936, -0.243379240830198, 1.69750790580363},
+        test_case{10.0, -2.0, 0.649677834014239, 0.760209650024628, 1.3579994757064},
+
+        // m = -5
+        test_case{-10.0, -5.0, 0.495527059808153, -0.868592501117692, 1.49255999377263},
+        test_case{-6.0, -5.0, 0.279115494901804, -0.960257538635194, 1.17878212468267},
+        test_case{-2.0, -5.0, 0.0894599315921725, -0.995990421961739, 1.01981145159406},
+        test_case{2.0, -5.0, -0.0894599315921725, -0.995990421961739, 1.01981145159406},
+        test_case{6.0, -5.0, -0.279115494901804, -0.960257538635194, 1.17878212468267},
+        test_case{10.0, -5.0, -0.495527059808153, -0.868592501117692, 1.49255999377263},
+
+        // m = -10
+        test_case{-10.0, -10.0, -0.673927384474905, 0.738797590991479, 2.35409880749553},
+        test_case{-6.0, -10.0, 0.377239038384813, 0.926115925744991, 1.55662870358187},
+        test_case{-2.0, -10.0, 0.518272042082259, -0.855215815099256, 1.91991122087485},
+        test_case{2.0, -10.0, -0.518272042082259, -0.855215815099256, 1.91991122087485},
+        test_case{6.0, -10.0, -0.377239038384813, 0.926115925744991, 1.55662870358187},
+        test_case{10.0, -10.0, 0.673927384474905, 0.738797590991479, 2.35409880749553},
+
+        // m = -0.5
+        test_case{-10.0, -0.5, 0.993960849894643, 0.109735267242208, 1.22228437180619},
+        test_case{-6.0, -0.5, -0.333655198670901, 0.942695183184831, 1.02745457116121},
+        test_case{-2.0, -0.5, -0.766580871421719, -0.642147777050048, 1.13746345708987},
+        test_case{2.0, -0.5, 0.766580871421719, -0.642147777050048, 1.13746345708987},
+        test_case{6.0, -0.5, 0.333655198670901, 0.942695183184831, 1.02745457116121},
+        test_case{10.0, -0.5, -0.993960849894643, 0.109735267242208, 1.22228437180619}
+    );
+
+    const double rtol = 1e-8;
+
+    double sn, cn, dn, ph;
+    int result = xsf::cephes::ellpj(u, m, &sn, &cn, &dn, &ph);
+
+    REQUIRE(result == 0); // Should succeed
+
+    const auto rel_error_sn = xsf::extended_relative_error(sn, ref_sn);
+    const auto rel_error_cn = xsf::extended_relative_error(cn, ref_cn);
+    const auto rel_error_dn = xsf::extended_relative_error(dn, ref_dn);
+    const auto rel_error_ph = xsf::extended_relative_error(ph, std::atan2(ref_sn, ref_cn));
+
+    CAPTURE(u, m, sn, ref_sn, rtol, rel_error_sn);
+    CAPTURE(u, m, cn, ref_cn, rtol, rel_error_cn);
+    CAPTURE(u, m, dn, ref_dn, rtol, rel_error_dn);
+
+    REQUIRE(rel_error_sn <= rtol);
+    REQUIRE(rel_error_cn <= rtol);
+    REQUIRE(rel_error_dn <= rtol);
+    REQUIRE(rel_error_ph <= rtol);
+}